14.5 What follows is the LP/IP code for problem 14-5 "Area restriction model" (ARM). The area restriction constraints begin with row 47 and continue to the "end". These rows will be modified and/or replaced to allow the achievement of the 120 acre, 90 acre, and 70 acre clearcut size restrictions. Currently, the ARM model constrains clearcuts to a maximum of 100 acres. Max 1088 X11 + 1096 X12 + 1104 X13 + 1112 X14 + 1120 X15 + 1126.4 X16 + 1132.8 X17 + 1139.2 X18 + 1145.6 X19 + 1152 X110 + 884 X21 + 890.5 X22 + 897 X23 + 903.5 X24 + 910 X25 + 915.2 X26 + 920.4 X27 + 925.6 X28 + 930.8 X29 + 936 X210 + 1183.2 X31 + 1191.9 X32 + 1200.6 X33 + 1209.3 X34 + 1218 X35 + 1224.96 X36 + 1231.92 X37 + 1238.88 X38 + 1245.84 X39 + 1252.8 X310 + 748 X41 + 753.5 X42 + 759 X43 + 764.5 X44 + 770 X45 + 774.4 X46 + 778.8 X47 + 783.2 X48 + 787.6 X49 + 792 X410 + 1407.6 X51 + 1417.95 X52 + 1428.3 X53 + 1438.65 X54 + 1449 X55 + 1457.28 X56 + 1465.56 X57 + 1473.84 X58 + 1482.12 X59 + 1490.4 X510 + 1693.2 X61 + 1705.65 X62 + 1718.1 X63 + 1730.55 X64 + 1743 X65 + 1752.96 X66 + 1762.92 X67 + 1772.88 X68 + 1782.84 X69 + 1792.8 X610 + 1298.8 X71 + 1308.35 X72 + 1317.9 X73 + 1327.45 X74 + 1337 X75 + 1344.64 X76 + 1352.28 X77 + 1359.92 X78 + 1367.56 X79 + 1375.2 X710 + 530.4 X81 + 534.3 X82 + 538.2 X83 + 542.1 X84 + 546 X85 + 549.12 X86 + 552.2401 X87 + 555.36 X88 + 558.48 X89 + 561.6 X810 + 1186.6 X91 + 1195.325 X92 + 1204.05 X93 + 1212.775 X94 + 1221.5 X95 + 1228.48 X96 + 1235.46 X97 + 1242.44 X98 + 1249.42 X99 + 1256.4 X910 + 877.2 X101 + 883.65 X102 + 890.1 X103 + 896.55 X104 + 903 X105 + 908.16 X106 + 913.32 X107 + 918.4799 X108 + 923.64 X109 + 928.8 X1010 + 1390.6 X111 + 1400.825 X112 + 1411.05 X113 + 1421.275 X114 + 1431.5 X115 + 1439.68 X116 + 1447.86 X117 + 1456.04 X118 + 1464.22 X119 + 1472.4 X1110 + 785.4 X121 + 791.175 X122 + 796.95 X123 + 802.725 X124 + 808.5 X125 + 813.1201 X126 + 817.7401 X127 + 822.36 X128 + 826.98 X129 + 831.6 X1210 + 1006.4 X131 + 1013.8 X132 + 1021.2 X133 + 1028.6 X134 + 1036 X135 + 1041.92 X136 + 1047.84 X137 + 1053.76 X138 + 1059.68 X139 + 1065.6 X1310 + 1655.8 X141 + 1667.975 X142 + 1680.15 X143 + 1692.325 X144 + 1704.5 X145 + 1714.24 X146 + 1723.98 X147 + 1733.72 X148 + 1743.46 X149 + 1753.2 X1410 + 2281.4 X151 + 2298.175 X152 + 2314.95 X153 + 2331.725 X154 + 2348.5 X155 + 2361.92 X156 + 2375.34 X157 + 2388.76 X158 + 2402.18 X159 + 2415.6 X1510 + 1887 X161 + 1900.875 X162 + 1914.75 X163 + 1928.625 X164 + 1942.5 X165 + 1953.6 X166 + 1964.7 X167 + 1975.8 X168 + 1986.9 X169 + 1998 X1610 + 1761.2 X171 + 1774.15 X172 + 1787.1 X173 + 1800.05 X174 + 1813 X175 + 1823.36 X176 + 1833.72 X177 + 1844.08 X178 + 1854.44 X179 + 1864.8 X1710 + 666.4 X181 + 671.3 X182 + 676.2 X183 + 681.1 X184 + 686 X185 + 689.92 X186 + 693.84 X187 + 697.76 X188 + 701.68 X189 + 705.6 X1810 + 1173 X191 + 1181.625 X192 + 1190.25 X193 + 1198.875 X194 + 1207.5 X195 + 1214.4 X196 + 1221.3 X197 + 1228.2 X198 + 1235.1 X199 + 1242 X1910 + 1115.2 X201 + 1123.4 X202 + 1131.6 X203 + 1139.8 X204 + 1148 X205 + 1154.56 X206 + 1161.12 X207 + 1167.68 X208 + 1174.24 X209 + 1180.8 X2010 + 1122 X211 + 1130.25 X212 + 1138.5 X213 + 1146.75 X214 + 1155 X215 + 1161.6 X216 + 1168.2 X217 + 1174.8 X218 + 1181.4 X219 + 1188 X2110 + 1955 X221 + 1969.375 X222 + 1983.75 X223 + 1998.125 X224 + 2012.5 X225 + 2024 X226 + 2035.5 X227 + 2047 X228 + 2058.5 X229 + 2070 X2210 + 1849.6 X231 + 1863.2 X232 + 1876.8 X233 + 1890.4 X234 + 1904 X235 + 1914.88 X236 + 1925.76 X237 + 1936.64 X238 + 1947.52 X239 + 1958.4 X2310 subject to 2) 32.0 X11 + 26.0 X21 + 34.8 X31 + 22.0 X41 + 41.4 X51 + 49.8 X61 + 38.2 X71 + 15.6 X81 + 34.9 X91 + 25.8 X101 + 40.9 X111 + 23.1 X121 + 29.6 X131 + 48.7 X141 + 67.1 X151 + 55.5 X161 + 51.8 X171 + 19.6 X181 + 34.5 X191 + 32.8 X201 + 33.0 X211 + 57.5 X221 + 54.4 X231 >= 50 3) 32.0 X12 + 26.0 X22 + 34.8 X32 + 22.0 X42 + 41.4 X52 + 49.8 X62 + 38.2 X72 + 15.6 X82 + 34.9 X92 + 25.8 X102 + 40.9 X112 + 23.1 X122 + 29.6 X132 + 48.7 X142 + 67.1 X152 + 55.5 X162 + 51.8 X172 + 19.6 X182 + 34.5 X192 + 32.8 X202 + 33.0 X212 + 57.5 X222 + 54.4 X232 >= 50 4) 32.0 X13 + 26.0 X23 + 34.8 X33 + 22.0 X43 + 41.4 X53 + 49.8 X63 + 38.2 X73 + 15.6 X83 + 34.9 X93 + 25.8 X103 + 40.9 X113 + 23.1 X123 + 29.6 X133 + 48.7 X143 + 67.1 X153 + 55.5 X163 + 51.8 X173 + 19.6 X183 + 34.5 X193 + 32.8 X203 + 33.0 X213 + 57.5 X223 + 54.4 X233 >= 50 5) 32.0 X14 + 26.0 X24 + 34.8 X34 + 22.0 X44 + 41.4 X54 + 49.8 X64 + 38.2 X74 + 15.6 X84 + 34.9 X94 + 25.8 X104 + 40.9 X114 + 23.1 X124 + 29.6 X134 + 48.7 X144 + 67.1 X154 + 55.5 X164 + 51.8 X174 + 19.6 X184 + 34.5 X194 + 32.8 X204 + 33.0 X214 + 57.5 X224 + 54.4 X234 >= 50 6) 32.0 X15 + 26.0 X25 + 34.8 X35 + 22.0 X45 + 41.4 X55 + 49.8 X65 + 38.2 X75 + 15.6 X85 + 34.9 X95 + 25.8 X105 + 40.9 X115 + 23.1 X125 + 29.6 X135 + 48.7 X145 + 67.1 X155 + 55.5 X165 + 51.8 X175 + 19.6 X185 + 34.5 X195 + 32.8 X205 + 33.0 X215 + 57.5 X225 + 54.4 X235 >= 50 7) 32.0 X16 + 26.0 X26 + 34.8 X36 + 22.0 X46 + 41.4 X56 + 49.8 X66 + 38.2 X76 + 15.6 X86 + 34.9 X96 + 25.8 X106 + 40.9 X116 + 23.1 X126 + 29.6 X136 + 48.7 X146 + 67.1 X156 + 55.5 X166 + 51.8 X176 + 19.6 X186 + 34.5 X196 + 32.8 X206 + 33.0 X216 + 57.5 X226 + 54.4 X236 >= 50 8) 32.0 X17 + 26.0 X27 + 34.8 X37 + 22.0 X47 + 41.4 X57 + 49.8 X67 + 38.2 X77 + 15.6 X87 + 34.9 X97 + 25.8 X107 + 40.9 X117 + 23.1 X127 + 29.6 X137 + 48.7 X147 + 67.1 X157 + 55.5 X167 + 51.8 X177 + 19.6 X187 + 34.5 X197 + 32.8 X207 + 33.0 X217 + 57.5 X227 + 54.4 X237 >= 50 9) 32.0 X18 + 26.0 X28 + 34.8 X38 + 22.0 X48 + 41.4 X58 + 49.8 X68 + 38.2 X78 + 15.6 X88 + 34.9 X98 + 25.8 X108 + 40.9 X118 + 23.1 X128 + 29.6 X138 + 48.7 X148 + 67.1 X158 + 55.5 X168 + 51.8 X178 + 19.6 X188 + 34.5 X198 + 32.8 X208 + 33.0 X218 + 57.5 X228 + 54.4 X238 >= 50 10) 32.0 X19 + 26.0 X29 + 34.8 X39 + 22.0 X49 + 41.4 X59 + 49.8 X69 + 38.2 X79 + 15.6 X89 + 34.9 X99 + 25.8 X109 + 40.9 X119 + 23.1 X129 + 29.6 X139 + 48.7 X149 + 67.1 X159 + 55.5 X169 + 51.8 X179 + 19.6 X189 + 34.5 X199 + 32.8 X209 + 33.0 X219 + 57.5 X229 + 54.4 X239 >= 50 11) 32.0 X110 + 26.0 X210 + 34.8 X310 + 22.0 X410 + 41.4 X510 + 49.8 X610 + 38.2 X710 + 15.6 X810 + 34.9 X910 + 25.8 X1010 + 40.9 X1110 + 23.1 X1210 + 29.6 X1310 + 48.7 X1410 + 67.1 X1510 + 55.5 X1610 + 51.8 X1710 + 19.6 X1810 + 34.5 X1910 + 32.8 X2010 + 33.0 X2110 + 57.5 X2210 + 54.4 X2310 >= 50 12) 32.0 X11 + 26.0 X21 + 34.8 X31 + 22.0 X41 + 41.4 X51 + 49.8 X61 + 38.2 X71 + 15.6 X81 + 34.9 X91 + 25.8 X101 + 40.9 X111 + 23.1 X121 + 29.6 X131 + 48.7 X141 + 67.1 X151 + 55.5 X161 + 51.8 X171 + 19.6 X181 + 34.5 X191 + 32.8 X201 + 33.0 X211 + 57.5 X221 + 54.4 X231 <= 70 13) 32.0 X12 + 26.0 X22 + 34.8 X32 + 22.0 X42 + 41.4 X52 + 49.8 X62 + 38.2 X72 + 15.6 X82 + 34.9 X92 + 25.8 X102 + 40.9 X112 + 23.1 X122 + 29.6 X132 + 48.7 X142 + 67.1 X152 + 55.5 X162 + 51.8 X172 + 19.6 X182 + 34.5 X192 + 32.8 X202 + 33.0 X212 + 57.5 X222 + 54.4 X232 <= 70 14) 32.0 X13 + 26.0 X23 + 34.8 X33 + 22.0 X43 + 41.4 X53 + 49.8 X63 + 38.2 X73 + 15.6 X83 + 34.9 X93 + 25.8 X103 + 40.9 X113 + 23.1 X123 + 29.6 X133 + 48.7 X143 + 67.1 X153 + 55.5 X163 + 51.8 X173 + 19.6 X183 + 34.5 X193 + 32.8 X203 + 33.0 X213 + 57.5 X223 + 54.4 X233 <= 70 15) 32.0 X14 + 26.0 X24 + 34.8 X34 + 22.0 X44 + 41.4 X54 + 49.8 X64 + 38.2 X74 + 15.6 X84 + 34.9 X94 + 25.8 X104 + 40.9 X114 + 23.1 X124 + 29.6 X134 + 48.7 X144 + 67.1 X154 + 55.5 X164 + 51.8 X174 + 19.6 X184 + 34.5 X194 + 32.8 X204 + 33.0 X214 + 57.5 X224 + 54.4 X234 <= 70 16) 32.0 X15 + 26.0 X25 + 34.8 X35 + 22.0 X45 + 41.4 X55 + 49.8 X65 + 38.2 X75 + 15.6 X85 + 34.9 X95 + 25.8 X105 + 40.9 X115 + 23.1 X125 + 29.6 X135 + 48.7 X145 + 67.1 X155 + 55.5 X165 + 51.8 X175 + 19.6 X185 + 34.5 X195 + 32.8 X205 + 33.0 X215 + 57.5 X225 + 54.4 X235 <= 70 17) 32.0 X16 + 26.0 X26 + 34.8 X36 + 22.0 X46 + 41.4 X56 + 49.8 X66 + 38.2 X76 + 15.6 X86 + 34.9 X96 + 25.8 X106 + 40.9 X116 + 23.1 X126 + 29.6 X136 + 48.7 X146 + 67.1 X156 + 55.5 X166 + 51.8 X176 + 19.6 X186 + 34.5 X196 + 32.8 X206 + 33.0 X216 + 57.5 X226 + 54.4 X236 <= 70 18) 32.0 X17 + 26.0 X27 + 34.8 X37 + 22.0 X47 + 41.4 X57 + 49.8 X67 + 38.2 X77 + 15.6 X87 + 34.9 X97 + 25.8 X107 + 40.9 X117 + 23.1 X127 + 29.6 X137 + 48.7 X147 + 67.1 X157 + 55.5 X167 + 51.8 X177 + 19.6 X187 + 34.5 X197 + 32.8 X207 + 33.0 X217 + 57.5 X227 + 54.4 X237 <= 70 19) 32.0 X18 + 26.0 X28 + 34.8 X38 + 22.0 X48 + 41.4 X58 + 49.8 X68 + 38.2 X78 + 15.6 X88 + 34.9 X98 + 25.8 X108 + 40.9 X118 + 23.1 X128 + 29.6 X138 + 48.7 X148 + 67.1 X158 + 55.5 X168 + 51.8 X178 + 19.6 X188 + 34.5 X198 + 32.8 X208 + 33.0 X218 + 57.5 X228 + 54.4 X238 <= 70 20) 32.0 X19 + 26.0 X29 + 34.8 X39 + 22.0 X49 + 41.4 X59 + 49.8 X69 + 38.2 X79 + 15.6 X89 + 34.9 X99 + 25.8 X109 + 40.9 X119 + 23.1 X129 + 29.6 X139 + 48.7 X149 + 67.1 X159 + 55.5 X169 + 51.8 X179 + 19.6 X189 + 34.5 X199 + 32.8 X209 + 33.0 X219 + 57.5 X229 + 54.4 X239 <= 70 21) 32.0 X110 + 26.0 X210 + 34.8 X310 + 22.0 X410 + 41.4 X510 + 49.8 X610 + 38.2 X710 + 15.6 X810 + 34.9 X910 + 25.8 X1010 + 40.9 X1110 + 23.1 X1210 + 29.6 X1310 + 48.7 X1410 + 67.1 X1510 + 55.5 X1610 + 51.8 X1710 + 19.6 X1810 + 34.5 X1910 + 32.8 X2010 + 33.0 X2110 + 57.5 X2210 + 54.4 X2310 <= 70 22) 32.0 X11 + 26.0 X21 + 34.8 X31 + 22.0 X41 + 41.4 X51 + 49.8 X61 + 38.2 X71 + 15.6 X81 + 34.9 X91 + 25.8 X101 + 40.9 X111 + 23.1 X121 + 29.6 X131 + 48.7 X141 + 67.1 X151 + 55.5 X161 + 51.8 X171 + 19.6 X181 + 34.5 X191 + 32.8 X201 + 33.0 X211 + 57.5 X221 + 54.4 X231 + 32.0 X12 + 26.0 X22 + 34.8 X32 + 22.0 X42 + 41.4 X52 + 49.8 X62 + 38.2 X72 + 15.6 X82 + 34.9 X92 + 25.8 X102 + 40.9 X112 + 23.1 X122 + 29.6 X132 + 48.7 X142 + 67.1 X152 + 55.5 X162 + 51.8 X172 + 19.6 X182 + 34.5 X192 + 32.8 X202 + 33.0 X212 + 57.5 X222 + 54.4 X232 + 32.0 X13 + 26.0 X23 + 34.8 X33 + 22.0 X43 + 41.4 X53 + 49.8 X63 + 38.2 X73 + 15.6 X83 + 34.9 X93 + 25.8 X103 + 40.9 X113 + 23.1 X123 + 29.6 X133 + 48.7 X143 + 67.1 X153 + 55.5 X163 + 51.8 X173 + 19.6 X183 + 34.5 X193 + 32.8 X203 + 33.0 X213 + 57.5 X223 + 54.4 X233 + 32.0 X14 + 26.0 X24 + 34.8 X34 + 22.0 X44 + 41.4 X54 + 49.8 X64 + 38.2 X74 + 15.6 X84 + 34.9 X94 + 25.8 X104 + 40.9 X114 + 23.1 X124 + 29.6 X134 + 48.7 X144 + 67.1 X154 + 55.5 X164 + 51.8 X174 + 19.6 X184 + 34.5 X194 + 32.8 X204 + 33.0 X214 + 57.5 X224 + 54.4 X234 + 32.0 X15 + 26.0 X25 + 34.8 X35 + 22.0 X45 + 41.4 X55 + 49.8 X65 + 38.2 X75 + 15.6 X85 + 34.9 X95 + 25.8 X105 + 40.9 X115 + 23.1 X125 + 29.6 X135 + 48.7 X145 + 67.1 X155 + 55.5 X165 + 51.8 X175 + 19.6 X185 + 34.5 X195 + 32.8 X205 + 33.0 X215 + 57.5 X225 + 54.4 X235 + 32.0 X16 + 26.0 X26 + 34.8 X36 + 22.0 X46 + 41.4 X56 + 49.8 X66 + 38.2 X76 + 15.6 X86 + 34.9 X96 + 25.8 X106 + 40.9 X116 + 23.1 X126 + 29.6 X136 + 48.7 X146 + 67.1 X156 + 55.5 X166 + 51.8 X176 + 19.6 X186 + 34.5 X196 + 32.8 X206 + 33.0 X216 + 57.5 X226 + 54.4 X236 + 32.0 X17 + 26.0 X27 + 34.8 X37 + 22.0 X47 + 41.4 X57 + 49.8 X67 + 38.2 X77 + 15.6 X87 + 34.9 X97 + 25.8 X107 + 40.9 X117 + 23.1 X127 + 29.6 X137 + 48.7 X147 + 67.1 X157 + 55.5 X167 + 51.8 X177 + 19.6 X187 + 34.5 X197 + 32.8 X207 + 33.0 X217 + 57.5 X227 + 54.4 X237 + 32.0 X18 + 26.0 X28 + 34.8 X38 + 22.0 X48 + 41.4 X58 + 49.8 X68 + 38.2 X78 + 15.6 X88 + 34.9 X98 + 25.8 X108 + 40.9 X118 + 23.1 X128 + 29.6 X138 + 48.7 X148 + 67.1 X158 + 55.5 X168 + 51.8 X178 + 19.6 X188 + 34.5 X198 + 32.8 X208 + 33.0 X218 + 57.5 X228 + 54.4 X238 + 32.0 X19 + 26.0 X29 + 34.8 X39 + 22.0 X49 + 41.4 X59 + 49.8 X69 + 38.2 X79 + 15.6 X89 + 34.9 X99 + 25.8 X109 + 40.9 X119 + 23.1 X129 + 29.6 X139 + 48.7 X149 + 67.1 X159 + 55.5 X169 + 51.8 X179 + 19.6 X189 + 34.5 X199 + 32.8 X209 + 33.0 X219 + 57.5 X229 + 54.4 X239 + 32.0 X110 + 26.0 X210 + 34.8 X310 + 22.0 X410 + 41.4 X510 + 49.8 X610 + 38.2 X710 + 15.6 X810 + 34.9 X910 + 25.8 X1010 + 40.9 X1110 + 23.1 X1210 + 29.6 X1310 + 48.7 X1410 + 67.1 X1510 + 55.5 X1610 + 51.8 X1710 + 19.6 X1810 + 34.5 X1910 + 32.8 X2010 + 33.0 X2110 + 57.5 X2210 + 54.4 X2310 <= 625 23) 32.0 X11 + 26.0 X21 + 34.8 X31 + 22.0 X41 + 41.4 X51 + 49.8 X61 + 38.2 X71 + 15.6 X81 + 34.9 X91 + 25.8 X101 + 40.9 X111 + 23.1 X121 + 29.6 X131 + 48.7 X141 + 67.1 X151 + 55.5 X161 + 51.8 X171 + 19.6 X181 + 34.5 X191 + 32.8 X201 + 33.0 X211 + 57.5 X221 + 54.4 X231 + 32.0 X12 + 26.0 X22 + 34.8 X32 + 22.0 X42 + 41.4 X52 + 49.8 X62 + 38.2 X72 + 15.6 X82 + 34.9 X92 + 25.8 X102 + 40.9 X112 + 23.1 X122 + 29.6 X132 + 48.7 X142 + 67.1 X152 + 55.5 X162 + 51.8 X172 + 19.6 X182 + 34.5 X192 + 32.8 X202 + 33.0 X212 + 57.5 X222 + 54.4 X232 + 32.0 X13 + 26.0 X23 + 34.8 X33 + 22.0 X43 + 41.4 X53 + 49.8 X63 + 38.2 X73 + 15.6 X83 + 34.9 X93 + 25.8 X103 + 40.9 X113 + 23.1 X123 + 29.6 X133 + 48.7 X143 + 67.1 X153 + 55.5 X163 + 51.8 X173 + 19.6 X183 + 34.5 X193 + 32.8 X203 + 33.0 X213 + 57.5 X223 + 54.4 X233 + 32.0 X14 + 26.0 X24 + 34.8 X34 + 22.0 X44 + 41.4 X54 + 49.8 X64 + 38.2 X74 + 15.6 X84 + 34.9 X94 + 25.8 X104 + 40.9 X114 + 23.1 X124 + 29.6 X134 + 48.7 X144 + 67.1 X154 + 55.5 X164 + 51.8 X174 + 19.6 X184 + 34.5 X194 + 32.8 X204 + 33.0 X214 + 57.5 X224 + 54.4 X234 + 32.0 X15 + 26.0 X25 + 34.8 X35 + 22.0 X45 + 41.4 X55 + 49.8 X65 + 38.2 X75 + 15.6 X85 + 34.9 X95 + 25.8 X105 + 40.9 X115 + 23.1 X125 + 29.6 X135 + 48.7 X145 + 67.1 X155 + 55.5 X165 + 51.8 X175 + 19.6 X185 + 34.5 X195 + 32.8 X205 + 33.0 X215 + 57.5 X225 + 54.4 X235 + 32.0 X16 + 26.0 X26 + 34.8 X36 + 22.0 X46 + 41.4 X56 + 49.8 X66 + 38.2 X76 + 15.6 X86 + 34.9 X96 + 25.8 X106 + 40.9 X116 + 23.1 X126 + 29.6 X136 + 48.7 X146 + 67.1 X156 + 55.5 X166 + 51.8 X176 + 19.6 X186 + 34.5 X196 + 32.8 X206 + 33.0 X216 + 57.5 X226 + 54.4 X236 + 32.0 X17 + 26.0 X27 + 34.8 X37 + 22.0 X47 + 41.4 X57 + 49.8 X67 + 38.2 X77 + 15.6 X87 + 34.9 X97 + 25.8 X107 + 40.9 X117 + 23.1 X127 + 29.6 X137 + 48.7 X147 + 67.1 X157 + 55.5 X167 + 51.8 X177 + 19.6 X187 + 34.5 X197 + 32.8 X207 + 33.0 X217 + 57.5 X227 + 54.4 X237 + 32.0 X18 + 26.0 X28 + 34.8 X38 + 22.0 X48 + 41.4 X58 + 49.8 X68 + 38.2 X78 + 15.6 X88 + 34.9 X98 + 25.8 X108 + 40.9 X118 + 23.1 X128 + 29.6 X138 + 48.7 X148 + 67.1 X158 + 55.5 X168 + 51.8 X178 + 19.6 X188 + 34.5 X198 + 32.8 X208 + 33.0 X218 + 57.5 X228 + 54.4 X238 + 32.0 X19 + 26.0 X29 + 34.8 X39 + 22.0 X49 + 41.4 X59 + 49.8 X69 + 38.2 X79 + 15.6 X89 + 34.9 X99 + 25.8 X109 + 40.9 X119 + 23.1 X129 + 29.6 X139 + 48.7 X149 + 67.1 X159 + 55.5 X169 + 51.8 X179 + 19.6 X189 + 34.5 X199 + 32.8 X209 + 33.0 X219 + 57.5 X229 + 54.4 X239 + 32.0 X110 + 26.0 X210 + 34.8 X310 + 22.0 X410 + 41.4 X510 + 49.8 X610 + 38.2 X710 + 15.6 X810 + 34.9 X910 + 25.8 X1010 + 40.9 X1110 + 23.1 X1210 + 29.6 X1310 + 48.7 X1410 + 67.1 X1510 + 55.5 X1610 + 51.8 X1710 + 19.6 X1810 + 34.5 X1910 + 32.8 X2010 + 33.0 X2110 + 57.5 X2210 + 54.4 X2310 >= 575 24) X11 + X12 + X13 + X14 + X15 + X16 + X17 + X18 + X19 + X110 <= 1 25) X21 + X22 + X23 + X24 + X25 + X26 + X27 + X28 + X29 + X210 <= 1 26) X31 + X32 + X33 + X34 + X35 + X36 + X37 + X38 + X39 + X310 <= 1 27) X41 + X42 + X43 + X44 + X45 + X46 + X47 + X48 + X49 + X410 <= 1 28) X51 + X52 + X53 + X54 + X55 + X56 + X57 + X58 + X59 + X510 <= 1 29) X61 + X62 + X63 + X64 + X65 + X66 + X67 + X68 + X69 + X610 <= 1 30) X71 + X72 + X73 + X74 + X75 + X76 + X77 + X78 + X79 + X710 <= 1 31) X81 + X82 + X83 + X84 + X85 + X86 + X87 + X88 + X89 + X810 <= 1 32) X91 + X92 + X93 + X94 + X95 + X96 + X97 + X98 + X99 + X910 <= 1 33) X101 + X102 + X103 + X104 + X105 + X106 + X107 + X108 + X109 + X1010 <= 1 34) X111 + X112 + X113 + X114 + X115 + X116 + X117 + X118 + X119 + X1110 <= 1 35) X121 + X122 + X123 + X124 + X125 + X126 + X127 + X128 + X129 + X1210 <= 1 36) X131 + X132 + X133 + X134 + X135 + X136 + X137 + X138 + X139 + X1310 <= 1 37) X141 + X142 + X143 + X144 + X145 + X146 + X147 + X148 + X149 + X1410 <= 1 38) X151 + X152 + X153 + X154 + X155 + X156 + X157 + X158 + X159 + X1510 <= 1 39) X161 + X162 + X163 + X164 + X165 + X166 + X167 + X168 + X169 + X1610 <= 1 40) X171 + X172 + X173 + X174 + X175 + X176 + X177 + X178 + X179 + X1710 <= 1 41) X181 + X182 + X183 + X184 + X185 + X186 + X187 + X188 + X189 + X1810 <= 1 42) X191 + X192 + X193 + X194 + X195 + X196 + X197 + X198 + X199 + X1910 <= 1 43) X201 + X202 + X203 + X204 + X205 + X206 + X207 + X208 + X209 + X2010 <= 1 44) X211 + X212 + X213 + X214 + X215 + X216 + X217 + X218 + X219 + X2110 <= 1 45) X221 + X222 + X223 + X224 + X225 + X226 + X227 + X228 + X229 + X2210 <= 1 46) X231 + X232 + X233 + X234 + X235 + X236 + X237 + X238 + X239 + X2310 <= 1 47) X51 + X61 + X62 + X63 + X64 + X65 + X71 + X72 + X73 + X74 + X75 <= 2 48) X52 + X61 + X62 + X63 + X64 + X65 + X66 + X71 + X72 + X73 + X74 + X75 + X76 <= 2 49) X53 + X61 + X62 + X63 + X64 + X65 + X66 + X67 + X71 + X72 + X73 + X74 + X75 + X76 + X77 <= 2 50) X54 + X61 + X62 + X63 + X64 + X65 + X66 + X67 + X68 + X71 + X72 + X73 + X74 + X75 + X76 + X77 + X78 <= 2 51) X55 + X61 + X62 + X63 + X64 + X65 + X66 + X67 + X68 + X69 + X71 + X72 + X73 + X74 + X75 + X76 + X77 + X78 + X79 <= 2 52) X56 + X62 + X63 + X64 + X65 + X66 + X67 + X68 + X69 + X610 + X72 + X73 + X74 + X75 + X76 + X77 + X78 + X79 + X710 <= 2 53) X57 + X63 + X64 + X65 + X66 + X67 + X68 + X69 + X610 + X73 + X74 + X75 + X76 + X77 + X78 + X79 + X710 <= 2 54) X58 + X64 + X65 + X66 + X67 + X68 + X69 + X610 + X74 + X75 + X76 + X77 + X78 + X79 + X710 <= 2 55) X59 + X65 + X66 + X67 + X68 + X69 + X610 + X75 + X76 + X77 + X78 + X79 + X710 <= 2 56) X510 + X66 + X67 + X68 + X69 + X610 + X76 + X77 + X78 + X79 + X710 <= 2 57) X141 + X151 + X152 + X153 + X154 + X155 <= 1 58) X142 + X151 + X152 + X153 + X154 + X155 + X156 <= 1 59) X143 + X151 + X152 + X153 + X154 + X155 + X156 + X157 <= 1 60) X144 + X151 + X152 + X153 + X154 + X155 + X156 + X157 + X158 <= 1 61) X145 + X151 + X152 + X153 + X154 + X155 + X156 + X157 + X158 + X159 <= 1 62) X146 + X152 + X153 + X154 + X155 + X156 + X157 + X158 + X159 + X1510 <= 1 63) X147 + X153 + X154 + X155 + X156 + X157 + X158 + X159 + X1510 <= 1 64) X148 + X154 + X155 + X156 + X157 + X158 + X159 + X1510 <= 1 65) X149 + X155 + X156 + X157 + X158 + X159 + X1510 <= 1 66) X1410 + X156 + X157 + X158 + X159 + X1510 <= 1 67) X161 + X171 + X172 + X173 + X174 + X175 <= 1 68) X162 + X171 + X172 + X173 + X174 + X175 + X176 <= 1 69) X163 + X171 + X172 + X173 + X174 + X175 + X176 + X177 <= 1 70) X164 + X171 + X172 + X173 + X174 + X175 + X176 + X177 + X178 <= 1 71) X165 + X171 + X172 + X173 + X174 + X175 + X176 + X177 + X178 + X179 <= 1 72) X166 + X172 + X173 + X174 + X175 + X176 + X177 + X178 + X179 + X1710 <= 1 73) X167 + X173 + X174 + X175 + X176 + X177 + X178 + X179 + X1710 <= 1 74) X168 + X174 + X175 + X176 + X177 + X178 + X179 + X1710 <= 1 75) X169 + X175 + X176 + X177 + X178 + X179 + X1710 <= 1 76) X1610 + X176 + X177 + X178 + X179 + X1710 <= 1 77) X171 + X181 + X182 + X183 + X184 + X185 + X191 + X192 + X193 + X194 + X195 <= 2 78) X172 + X181 + X182 + X183 + X184 + X185 + X186 + X191 + X192 + X193 + X194 + X195 + X196 <= 2 79) X173 + X181 + X182 + X183 + X184 + X185 + X186 + X187 + X191 + X192 + X193 + X194 + X195 + X196 + X197 <= 2 80) X174 + X181 + X182 + X183 + X184 + X185 + X186 + X187 + X188 + X191 + X192 + X193 + X194 + X195 + X196 + X197 + X198 <= 2 81) X175 + X181 + X182 + X183 + X184 + X185 + X186 + X187 + X188 + X189 + X191 + X192 + X193 + X194 + X195 + X196 + X197 + X198 + X199 <= 2 82) X176 + X182 + X183 + X184 + X185 + X186 + X187 + X188 + X189 + X1810 + X192 + X193 + X194 + X195 + X196 + X197 + X198 + X199 + X1910 <= 2 83) X177 + X183 + X184 + X185 + X186 + X187 + X188 + X189 + X1810 + X193 + X194 + X195 + X196 + X197 + X198 + X199 + X1910 <= 2 84) X178 + X184 + X185 + X186 + X187 + X188 + X189 + X1810 + X194 + X195 + X196 + X197 + X198 + X199 + X1910 <= 2 85) X179 + X185 + X186 + X187 + X188 + X189 + X1810 + X195 + X196 + X197 + X198 + X199 + X1910 <= 2 86) X1710 + X186 + X187 + X188 + X189 + X1810 + X196 + X197 + X198 + X199 + X1910 <= 2 87) X191 + X201 + X202 + X203 + X204 + X205 + X211 + X212 + X213 + X214 + X215 <= 2 88) X192 + X201 + X202 + X203 + X204 + X205 + X206 + X211 + X212 + X213 + X214 + X215 + X216 <= 2 89) X193 + X201 + X202 + X203 + X204 + X205 + X206 + X207 + X211 + X212 + X213 + X214 + X215 + X216 + X217 <= 2 90) X194 + X201 + X202 + X203 + X204 + X205 + X206 + X207 + X208 + X211 + X212 + X213 + X214 + X215 + X216 + X217 + X218 <= 2 91) X195 + X201 + X202 + X203 + X204 + X205 + X206 + X207 + X208 + X209 + X211 + X212 + X213 + X214 + X215 + X216 + X217 + X218 + X219 <= 2 92) X196 + X202 + X203 + X204 + X205 + X206 + X207 + X208 + X209 + X2010 + X212 + X213 + X214 + X215 + X216 + X217 + X218 + X219 + X2110 <= 2 93) X197 + X203 + X204 + X205 + X206 + X207 + X208 + X209 + X2010 + X213 + X214 + X215 + X216 + X217 + X218 + X219 + X2110 <= 2 94) X198 + X204 + X205 + X206 + X207 + X208 + X209 + X2010 + X214 + X215 + X216 + X217 + X218 + X219 + X2110 <= 2 95) X199 + X205 + X206 + X207 + X208 + X209 + X2010 + X215 + X216 + X217 + X218 + X219 + X2110 <= 2 96) X1910 + X206 + X207 + X208 + X209 + X2010 + X216 + X217 + X218 + X219 + X2110 <= 2 97) X221 + X231 + X232 + X233 + X234 + X235 <= 1 98) X222 + X231 + X232 + X233 + X234 + X235 + X236 <= 1 99) X223 + X231 + X232 + X233 + X234 + X235 + X236 + X237 <= 1 100) X224 + X231 + X232 + X233 + X234 + X235 + X236 + X237 + X238 <= 1 101) X225 + X231 + X232 + X233 + X234 + X235 + X236 + X237 + X238 + X239 <= 1 102) X226 + X232 + X233 + X234 + X235 + X236 + X237 + X238 + X239 + X2310 <= 1 103) X227 + X233 + X234 + X235 + X236 + X237 + X238 + X239 + X2310 <= 1 104) X228 + X234 + X235 + X236 + X237 + X238 + X239 + X2310 <= 1 105) X229 + X235 + X236 + X237 + X238 + X239 + X2310 <= 1 106) X2210 + X236 + X237 + X238 + X239 + X2310 <= 1 end inte X11 inte X12 inte X13 inte X14 inte X15 inte X16 inte X17 inte X18 inte X19 inte X110 inte X21 inte X22 inte X23 inte X24 inte X25 inte X26 inte X27 inte X28 inte X29 inte X210 inte X31 inte X32 inte X33 inte X34 inte X35 inte X36 inte X37 inte X38 inte X39 inte X310 inte X41 inte X42 inte X43 inte X44 inte X45 inte X46 inte X47 inte X48 inte X49 inte X410 inte X51 inte X52 inte X53 inte X54 inte X55 inte X56 inte X57 inte X58 inte X59 inte X510 inte X61 inte X62 inte X63 inte X64 inte X65 inte X66 inte X67 inte X68 inte X69 inte X610 inte X71 inte X72 inte X73 inte X74 inte X75 inte X76 inte X77 inte X78 inte X79 inte X710 inte X81 inte X82 inte X83 inte X84 inte X85 inte X86 inte X87 inte X88 inte X89 inte X810 inte X91 inte X92 inte X93 inte X94 inte X95 inte X96 inte X97 inte X98 inte X99 inte X910 inte X101 inte X102 inte X103 inte X104 inte X105 inte X106 inte X107 inte X108 inte X109 inte X1010 inte X111 inte X112 inte X113 inte X114 inte X115 inte X116 inte X117 inte X118 inte X119 inte X1110 inte X121 inte X122 inte X123 inte X124 inte X125 inte X126 inte X127 inte X128 inte X129 inte X1210 inte X131 inte X132 inte X133 inte X134 inte X135 inte X136 inte X137 inte X138 inte X139 inte X1310 inte X141 inte X142 inte X143 inte X144 inte X145 inte X146 inte X147 inte X148 inte X149 inte X1410 inte X151 inte X152 inte X153 inte X154 inte X155 inte X156 inte X157 inte X158 inte X159 inte X1510 inte X161 inte X162 inte X163 inte X164 inte X165 inte X166 inte X167 inte X168 inte X169 inte X1610 inte X171 inte X172 inte X173 inte X174 inte X175 inte X176 inte X177 inte X178 inte X179 inte X1710 inte X181 inte X182 inte X183 inte X184 inte X185 inte X186 inte X187 inte X188 inte X189 inte X1810 inte X191 inte X192 inte X193 inte X194 inte X195 inte X196 inte X197 inte X198 inte X199 inte X1910 inte X201 inte X202 inte X203 inte X204 inte X205 inte X206 inte X207 inte X208 inte X209 inte X2010 inte X211 inte X212 inte X213 inte X214 inte X215 inte X216 inte X217 inte X218 inte X219 inte X2110 inte X221 inte X222 inte X223 inte X224 inte X225 inte X226 inte X227 inte X228 inte X229 inte X2210 inte X231 inte X232 inte X233 inte X234 inte X235 inte X236 inte X237 inte X238 inte X239 inte X2310 Problem 14-5. (a) 120 acre clearcut size restriction. Rows 47-56: keep the same as in 100 acre problem. Rows 57-66: Add unit 13, then allow 2 units to be harvested (of units 13,14, and 15) in any one 5-year period. Rows 67-76: Add unit 18, then allow 2 units to be harvested (of units 16,17, and 18) in any one 5-year period. Rows 77-86: Add unit 20, then allow 3 units to be harvested (of units 17,18,19, and 20) in any one 5-year period. Rows 87-106: Delete, no longer relevant in 120 acre problem. Here are the ARM constraints: 47) X51 + X61 + X62 + X63 + X64 + X65 + X71 + X72 + X73 + X74 + X75 <= 2 48) X52 + X61 + X62 + X63 + X64 + X65 + X66 + X71 + X72 + X73 + X74 + X75 + X76 <= 2 49) X53 + X61 + X62 + X63 + X64 + X65 + X66 + X67 + X71 + X72 + X73 + X74 + X75 + X76 + X77 <= 2 50) X54 + X61 + X62 + X63 + X64 + X65 + X66 + X67 + X68 + X71 + X72 + X73 + X74 + X75 + X76 + X77 + X78 <= 2 51) X55 + X61 + X62 + X63 + X64 + X65 + X66 + X67 + X68 + X69 + X71 + X72 + X73 + X74 + X75 + X76 + X77 + X78 + X79 <= 2 52) X56 + X62 + X63 + X64 + X65 + X66 + X67 + X68 + X69 + X610 + X72 + X73 + X74 + X75 + X76 + X77 + X78 + X79 + X710 <= 2 53) X57 + X63 + X64 + X65 + X66 + X67 + X68 + X69 + X610 + X73 + X74 + X75 + X76 + X77 + X78 + X79 + X710 <= 2 54) X58 + X64 + X65 + X66 + X67 + X68 + X69 + X610 + X74 + X75 + X76 + X77 + X78 + X79 + X710 <= 2 55) X59 + X65 + X66 + X67 + X68 + X69 + X610 + X75 + X76 + X77 + X78 + X79 + X710 <= 2 56) X510 + X66 + X67 + X68 + X69 + X610 + X76 + X77 + X78 + X79 + X710 <= 2 57) X141 + X151 + X152 + X153 + X154 + X155 + X131 + X132 + X133 + X134 + X135 <= 2 58) X142 + X151 + X152 + X153 + X154 + X155 + X156 + X131 + X132 + X133 + X134 + X135 + X136 <= 2 59) X143 + X151 + X152 + X153 + X154 + X155 + X156 + X157 + X131 + X132 + X133 + X134 + X135 + X136 + X137 <= 2 60) X144 + X151 + X152 + X153 + X154 + X155 + X156 + X157 + X158 + X131 + X132 + X133 + X134 + X135 + X136 + X137 + X138 <= 2 61) X145 + X151 + X152 + X153 + X154 + X155 + X156 + X157 + X158 + X159 + X131 + X132 + X133 + X134 + X135 + X136 + X137 + X138 + X139 <= 2 62) X146 + X152 + X153 + X154 + X155 + X156 + X157 + X158 + X159 + X1510 + X132 + X133 + X134 + X135 + X136 + X137 + X138 + X139 + X1310 <= 2 63) X147 + X153 + X154 + X155 + X156 + X157 + X158 + X159 + X1510 + X133 + X134 + X135 + X136 + X137 + X138 + X139 + X1310 <= 2 64) X148 + X154 + X155 + X156 + X157 + X158 + X159 + X1510 + X134 + X135 + X136 + X137 + X138 + X139 + X1310 <= 2 65) X149 + X155 + X156 + X157 + X158 + X159 + X1510 + X135 + X136 + X137 + X138 + X139 + X1310 <= 2 66) X1410 + X156 + X157 + X158 + X159 + X1510 + X136 + X137 + X138 + X139 + X1310 <= 2 67) X161 + X171 + X172 + X173 + X174 + X175 + X181 + X182 + X183 + X184 + X185 <= 2 68) X162 + X171 + X172 + X173 + X174 + X175 + X176 + X181 + X182 + X183 + X184 + X185 + X186 <= 2 69) X163 + X171 + X172 + X173 + X174 + X175 + X176 + X177 + X181 + X182 + X183 + X184 + X185 + X186 + X187 <= 2 70) X164 + X171 + X172 + X173 + X174 + X175 + X176 + X177 + X178 + X181 + X182 + X183 + X184 + X185 + X186 + X187 + X188 <= 2 71) X165 + X171 + X172 + X173 + X174 + X175 + X176 + X177 + X178 + X179 + X181 + X182 + X183 + X184 + X185 + X186 + X187 + X188 + X189 <= 2 72) X166 + X172 + X173 + X174 + X175 + X176 + X177 + X178 + X179 + X1710 + X182 + X183 + X184 + X185 + X186 + X187 + X188 + X189 + X1810 <= 2 73) X167 + X173 + X174 + X175 + X176 + X177 + X178 + X179 + X1710 + X183 + X184 + X185 + X186 + X187 + X188 + X189 + X1810 <= 2 74) X168 + X174 + X175 + X176 + X177 + X178 + X179 + X1710 + X184 + X185 + X186 + X187 + X188 + X189 + X1810 <= 2 75) X169 + X175 + X176 + X177 + X178 + X179 + X1710 + X185 + X186 + X187 + X188 + X189 + X1810 <= 2 76) X1610 + X176 + X177 + X178 + X179 + X1710 + X186 + X187 + X188 + X189 + X1810 <= 2 77) X171 + X181 + X182 + X183 + X184 + X185 + X191 + X192 + X193 + X194 + X195 + X201 + X202 + X203 + X204 + X205 <= 3 78) X172 + X181 + X182 + X183 + X184 + X185 + X186 + X191 + X192 + X193 + X194 + X195 + X196 + X201 + X202 + X203 + X204 + X205 + X206 <= 3 79) X173 + X181 + X182 + X183 + X184 + X185 + X186 + X187 + X191 + X192 + X193 + X194 + X195 + X196 + X197 + X201 + X202 + X203 + X204 + X205 + X206 + X207 <= 3 80) X174 + X181 + X182 + X183 + X184 + X185 + X186 + X187 + X188 + X191 + X192 + X193 + X194 + X195 + X196 + X197 + X198 + X201 + X202 + X203 + X204 + X205 + X206 + X207 + X208 <= 3 81) X175 + X181 + X182 + X183 + X184 + X185 + X186 + X187 + X188 + X189 + X191 + X192 + X193 + X194 + X195 + X196 + X197 + X198 + X199 + X201 + X202 + X203 + X204 + X205 + X206 + X207 + X208 + X209 <= 3 82) X176 + X182 + X183 + X184 + X185 + X186 + X187 + X188 + X189 + X1810 + X192 + X193 + X194 + X195 + X196 + X197 + X198 + X199 + X1910 + X202 + X203 + X204 + X205 + X206 + X207 + X208 + X209 + X2010 <= 3 83) X177 + X183 + X184 + X185 + X186 + X187 + X188 + X189 + X1810 + X193 + X194 + X195 + X196 + X197 + X198 + X199 + X1910 + X203 + X204 + X205 + X206 + X207 + X208 + X209 + X2010 <= 3 84) X178 + X184 + X185 + X186 + X187 + X188 + X189 + X1810 + X194 + X195 + X196 + X197 + X198 + X199 + X1910 + X204 + X205 + X206 + X207 + X208 + X209 + X2010 <= 3 85) X179 + X185 + X186 + X187 + X188 + X189 + X1810 + X195 + X196 + X197 + X198 + X199 + X1910 + X205 + X206 + X207 + X208 + X209 + X2010 <= 3 86) X1710 + X186 + X187 + X188 + X189 + X1810 + X196 + X197 + X198 + X199 + X1910 + X206 + X207 + X208 + X209 + X2010 <= 3 end Problem 14-5. (b) 90 acre clearcut size restriction. Rows 47-106: keep the same as in 100 acre problem. Rows 107-116: Add constraints to allow only unit 5 or unit 6 to be harvested in any one 5-year period. Here are the ARM constraints: 47) X51 + X61 + X62 + X63 + X64 + X65 + X71 + X72 + X73 + X74 + X75 <= 2 48) X52 + X61 + X62 + X63 + X64 + X65 + X66 + X71 + X72 + X73 + X74 + X75 + X76 <= 2 49) X53 + X61 + X62 + X63 + X64 + X65 + X66 + X67 + X71 + X72 + X73 + X74 + X75 + X76 + X77 <= 2 50) X54 + X61 + X62 + X63 + X64 + X65 + X66 + X67 + X68 + X71 + X72 + X73 + X74 + X75 + X76 + X77 + X78 <= 2 51) X55 + X61 + X62 + X63 + X64 + X65 + X66 + X67 + X68 + X69 + X71 + X72 + X73 + X74 + X75 + X76 + X77 + X78 + X79 <= 2 52) X56 + X62 + X63 + X64 + X65 + X66 + X67 + X68 + X69 + X610 + X72 + X73 + X74 + X75 + X76 + X77 + X78 + X79 + X710 <= 2 53) X57 + X63 + X64 + X65 + X66 + X67 + X68 + X69 + X610 + X73 + X74 + X75 + X76 + X77 + X78 + X79 + X710 <= 2 54) X58 + X64 + X65 + X66 + X67 + X68 + X69 + X610 + X74 + X75 + X76 + X77 + X78 + X79 + X710 <= 2 55) X59 + X65 + X66 + X67 + X68 + X69 + X610 + X75 + X76 + X77 + X78 + X79 + X710 <= 2 56) X510 + X66 + X67 + X68 + X69 + X610 + X76 + X77 + X78 + X79 + X710 <= 2 57) X141 + X151 + X152 + X153 + X154 + X155 <= 1 58) X142 + X151 + X152 + X153 + X154 + X155 + X156 <= 1 59) X143 + X151 + X152 + X153 + X154 + X155 + X156 + X157 <= 1 60) X144 + X151 + X152 + X153 + X154 + X155 + X156 + X157 + X158 <= 1 61) X145 + X151 + X152 + X153 + X154 + X155 + X156 + X157 + X158 + X159 <= 1 62) X146 + X152 + X153 + X154 + X155 + X156 + X157 + X158 + X159 + X1510 <= 1 63) X147 + X153 + X154 + X155 + X156 + X157 + X158 + X159 + X1510 <= 1 64) X148 + X154 + X155 + X156 + X157 + X158 + X159 + X1510 <= 1 65) X149 + X155 + X156 + X157 + X158 + X159 + X1510 <= 1 66) X1410 + X156 + X157 + X158 + X159 + X1510 <= 1 67) X161 + X171 + X172 + X173 + X174 + X175 <= 1 68) X162 + X171 + X172 + X173 + X174 + X175 + X176 <= 1 69) X163 + X171 + X172 + X173 + X174 + X175 + X176 + X177 <= 1 70) X164 + X171 + X172 + X173 + X174 + X175 + X176 + X177 + X178 <= 1 71) X165 + X171 + X172 + X173 + X174 + X175 + X176 + X177 + X178 + X179 <= 1 72) X166 + X172 + X173 + X174 + X175 + X176 + X177 + X178 + X179 + X1710 <= 1 73) X167 + X173 + X174 + X175 + X176 + X177 + X178 + X179 + X1710 <= 1 74) X168 + X174 + X175 + X176 + X177 + X178 + X179 + X1710 <= 1 75) X169 + X175 + X176 + X177 + X178 + X179 + X1710 <= 1 76) X1610 + X176 + X177 + X178 + X179 + X1710 <= 1 77) X171 + X181 + X182 + X183 + X184 + X185 + X191 + X192 + X193 + X194 + X195 <= 2 78) X172 + X181 + X182 + X183 + X184 + X185 + X186 + X191 + X192 + X193 + X194 + X195 + X196 <= 2 79) X173 + X181 + X182 + X183 + X184 + X185 + X186 + X187 + X191 + X192 + X193 + X194 + X195 + X196 + X197 <= 2 80) X174 + X181 + X182 + X183 + X184 + X185 + X186 + X187 + X188 + X191 + X192 + X193 + X194 + X195 + X196 + X197 + X198 <= 2 81) X175 + X181 + X182 + X183 + X184 + X185 + X186 + X187 + X188 + X189 + X191 + X192 + X193 + X194 + X195 + X196 + X197 + X198 + X199 <= 2 82) X176 + X182 + X183 + X184 + X185 + X186 + X187 + X188 + X189 + X1810 + X192 + X193 + X194 + X195 + X196 + X197 + X198 + X199 + X1910 <= 2 83) X177 + X183 + X184 + X185 + X186 + X187 + X188 + X189 + X1810 + X193 + X194 + X195 + X196 + X197 + X198 + X199 + X1910 <= 2 84) X178 + X184 + X185 + X186 + X187 + X188 + X189 + X1810 + X194 + X195 + X196 + X197 + X198 + X199 + X1910 <= 2 85) X179 + X185 + X186 + X187 + X188 + X189 + X1810 + X195 + X196 + X197 + X198 + X199 + X1910 <= 2 86) X1710 + X186 + X187 + X188 + X189 + X1810 + X196 + X197 + X198 + X199 + X1910 <= 2 87) X191 + X201 + X202 + X203 + X204 + X205 + X211 + X212 + X213 + X214 + X215 <= 2 88) X192 + X201 + X202 + X203 + X204 + X205 + X206 + X211 + X212 + X213 + X214 + X215 + X216 <= 2 89) X193 + X201 + X202 + X203 + X204 + X205 + X206 + X207 + X211 + X212 + X213 + X214 + X215 + X216 + X217 <= 2 90) X194 + X201 + X202 + X203 + X204 + X205 + X206 + X207 + X208 + X211 + X212 + X213 + X214 + X215 + X216 + X217 + X218 <= 2 91) X195 + X201 + X202 + X203 + X204 + X205 + X206 + X207 + X208 + X209 + X211 + X212 + X213 + X214 + X215 + X216 + X217 + X218 + X219 <= 2 92) X196 + X202 + X203 + X204 + X205 + X206 + X207 + X208 + X209 + X2010 + X212 + X213 + X214 + X215 + X216 + X217 + X218 + X219 + X2110 <= 2 93) X197 + X203 + X204 + X205 + X206 + X207 + X208 + X209 + X2010 + X213 + X214 + X215 + X216 + X217 + X218 + X219 + X2110 <= 2 94) X198 + X204 + X205 + X206 + X207 + X208 + X209 + X2010 + X214 + X215 + X216 + X217 + X218 + X219 + X2110 <= 2 95) X199 + X205 + X206 + X207 + X208 + X209 + X2010 + X215 + X216 + X217 + X218 + X219 + X2110 <= 2 96) X1910 + X206 + X207 + X208 + X209 + X2010 + X216 + X217 + X218 + X219 + X2110 <= 2 97) X221 + X231 + X232 + X233 + X234 + X235 <= 1 98) X222 + X231 + X232 + X233 + X234 + X235 + X236 <= 1 99) X223 + X231 + X232 + X233 + X234 + X235 + X236 + X237 <= 1 100) X224 + X231 + X232 + X233 + X234 + X235 + X236 + X237 + X238 <= 1 101) X225 + X231 + X232 + X233 + X234 + X235 + X236 + X237 + X238 + X239 <= 1 102) X226 + X232 + X233 + X234 + X235 + X236 + X237 + X238 + X239 + X2310 <= 1 103) X227 + X233 + X234 + X235 + X236 + X237 + X238 + X239 + X2310 <= 1 104) X228 + X234 + X235 + X236 + X237 + X238 + X239 + X2310 <= 1 105) X229 + X235 + X236 + X237 + X238 + X239 + X2310 <= 1 106) X2210 + X236 + X237 + X238 + X239 + X2310 <= 1 107) X51 + X61 + X62 + X63 + X64 + X65 <= 1 108) X52 + X61 + X62 + X63 + X64 + X65 + X66 <= 1 109) X53 + X61 + X62 + X63 + X64 + X65 + X66 + X67 <= 1 110) X54 + X61 + X62 + X63 + X64 + X65 + X66 + X67 + X68 <= 1 111) X55 + X61 + X62 + X63 + X64 + X65 + X66 + X67 + X68 + X69 <= 1 112) X56 + X62 + X63 + X64 + X65 + X66 + X67 + X68 + X69 + X610 <= 1 113) X57 + X63 + X64 + X65 + X66 + X67 + X68 + X69 + X610 <= 1 114) X58 + X64 + X65 + X66 + X67 + X68 + X69 + X610 <= 1 115) X59 + X65 + X66 + X67 + X68 + X69 + X610 <= 1 116) X510 + X66 + X67 + X68 + X69 + X610 <= 1 end Problem 14-5. (c) 70 acre clearcut size restriction. Rows 47-56: Delete constraints from 100 acre problem, since we no longer need to control units 5,6, and 7 together. We will control 5 & 6, then 6 & 7, with constraints in rows 107-126. Add constraints here to allow only unit 13 or unit 14 to be harvested in any one 5-year period. Rows 57-66: Keep the same as in 100 acre problem. Rows 67-76: Keep the same as in 100 acre problem. Rows 77-86: Remove unit 19 from these constraints, then change <=2 to <=1. We no longer control 17,18, and 19 together, but just 17 and 18. Rows 87-96: Keep the same as in 100 acre problem. Rows 97-106: Keep the same as in 100 acre problem. Rows 107-116: Add constraints to allow only unit 5 or unit 6 to be harvested in any one 5-year period. Rows 117-126: Add constraints to allow only unit 6 or unit 7 to be harvested in any one 5-year period. Rows 127-136: Add constraints to allow 2 units to be harvested of units 18,19, and 20 in any one 5-year period. Here are the ARM constraints: 47) X131 + X141 + X142 + X143 + X144 + X145 <= 1 48) X132 + X141 + X142 + X143 + X144 + X145 + X146 <= 1 49) X133 + X141 + X142 + X143 + X144 + X145 + X146 + X147 <= 1 50) X134 + X141 + X142 + X143 + X144 + X145 + X146 + X147 + X148 <= 1 51) X135 + X141 + X142 + X143 + X144 + X145 + X146 + X147 + X148 + X149 <= 1 52) X136 + X142 + X143 + X144 + X145 + X146 + X147 + X148 + X149 + X1410 <= 1 53) X137 + X143 + X144 + X145 + X146 + X147 + X148 + X149 + X1410 <= 1 54) X138 + X144 + X145 + X146 + X147 + X148 + X149 + X1410 <= 1 55) X139 + X145 + X146 + X147 + X148 + X149 + X1410 <= 1 56) X1310 + X146 + X147 + X148 + X149 + X1410 <= 1 57) X141 + X151 + X152 + X153 + X154 + X155 <= 1 58) X142 + X151 + X152 + X153 + X154 + X155 + X156 <= 1 59) X143 + X151 + X152 + X153 + X154 + X155 + X156 + X157 <= 1 60) X144 + X151 + X152 + X153 + X154 + X155 + X156 + X157 + X158 <= 1 61) X145 + X151 + X152 + X153 + X154 + X155 + X156 + X157 + X158 + X159 <= 1 62) X146 + X152 + X153 + X154 + X155 + X156 + X157 + X158 + X159 + X1510 <= 1 63) X147 + X153 + X154 + X155 + X156 + X157 + X158 + X159 + X1510 <= 1 64) X148 + X154 + X155 + X156 + X157 + X158 + X159 + X1510 <= 1 65) X149 + X155 + X156 + X157 + X158 + X159 + X1510 <= 1 66) X1410 + X156 + X157 + X158 + X159 + X1510 <= 1 67) X161 + X171 + X172 + X173 + X174 + X175 <= 1 68) X162 + X171 + X172 + X173 + X174 + X175 + X176 <= 1 69) X163 + X171 + X172 + X173 + X174 + X175 + X176 + X177 <= 1 70) X164 + X171 + X172 + X173 + X174 + X175 + X176 + X177 + X178 <= 1 71) X165 + X171 + X172 + X173 + X174 + X175 + X176 + X177 + X178 + X179 <= 1 72) X166 + X172 + X173 + X174 + X175 + X176 + X177 + X178 + X179 + X1710 <= 1 73) X167 + X173 + X174 + X175 + X176 + X177 + X178 + X179 + X1710 <= 1 74) X168 + X174 + X175 + X176 + X177 + X178 + X179 + X1710 <= 1 75) X169 + X175 + X176 + X177 + X178 + X179 + X1710 <= 1 76) X1610 + X176 + X177 + X178 + X179 + X1710 <= 1 77) X171 + X181 + X182 + X183 + X184 + X185 <= 1 78) X172 + X181 + X182 + X183 + X184 + X185 + X186 <= 1 79) X173 + X181 + X182 + X183 + X184 + X185 + X186 + X187 <= 1 80) X174 + X181 + X182 + X183 + X184 + X185 + X186 + X187 + X188 <= 1 81) X175 + X181 + X182 + X183 + X184 + X185 + X186 + X187 + X188 + X189 <= 1 82) X176 + X182 + X183 + X184 + X185 + X186 + X187 + X188 + X189 + X1810 <= 1 83) X177 + X183 + X184 + X185 + X186 + X187 + X188 + X189 + X1810 <= 1 84) X178 + X184 + X185 + X186 + X187 + X188 + X189 + X1810 <= 1 85) X179 + X185 + X186 + X187 + X188 + X189 + X1810 <= 1 86) X1710 + X186 + X187 + X188 + X189 + X1810 <= 1 87) X191 + X201 + X202 + X203 + X204 + X205 + X211 + X212 + X213 + X214 + X215 <= 2 88) X192 + X201 + X202 + X203 + X204 + X205 + X206 + X211 + X212 + X213 + X214 + X215 + X216 <= 2 89) X193 + X201 + X202 + X203 + X204 + X205 + X206 + X207 + X211 + X212 + X213 + X214 + X215 + X216 + X217 <= 2 90) X194 + X201 + X202 + X203 + X204 + X205 + X206 + X207 + X208 + X211 + X212 + X213 + X214 + X215 + X216 + X217 + X218 <= 2 91) X195 + X201 + X202 + X203 + X204 + X205 + X206 + X207 + X208 + X209 + X211 + X212 + X213 + X214 + X215 + X216 + X217 + X218 + X219 <= 2 92) X196 + X202 + X203 + X204 + X205 + X206 + X207 + X208 + X209 + X2010 + X212 + X213 + X214 + X215 + X216 + X217 + X218 + X219 + X2110 <= 2 93) X197 + X203 + X204 + X205 + X206 + X207 + X208 + X209 + X2010 + X213 + X214 + X215 + X216 + X217 + X218 + X219 + X2110 <= 2 94) X198 + X204 + X205 + X206 + X207 + X208 + X209 + X2010 + X214 + X215 + X216 + X217 + X218 + X219 + X2110 <= 2 95) X199 + X205 + X206 + X207 + X208 + X209 + X2010 + X215 + X216 + X217 + X218 + X219 + X2110 <= 2 96) X1910 + X206 + X207 + X208 + X209 + X2010 + X216 + X217 + X218 + X219 + X2110 <= 2 97) X221 + X231 + X232 + X233 + X234 + X235 <= 1 98) X222 + X231 + X232 + X233 + X234 + X235 + X236 <= 1 99) X223 + X231 + X232 + X233 + X234 + X235 + X236 + X237 <= 1 100) X224 + X231 + X232 + X233 + X234 + X235 + X236 + X237 + X238 <= 1 101) X225 + X231 + X232 + X233 + X234 + X235 + X236 + X237 + X238 + X239 <= 1 102) X226 + X232 + X233 + X234 + X235 + X236 + X237 + X238 + X239 + X2310 <= 1 103) X227 + X233 + X234 + X235 + X236 + X237 + X238 + X239 + X2310 <= 1 104) X228 + X234 + X235 + X236 + X237 + X238 + X239 + X2310 <= 1 105) X229 + X235 + X236 + X237 + X238 + X239 + X2310 <= 1 106) X2210 + X236 + X237 + X238 + X239 + X2310 <= 1 107) X51 + X61 + X62 + X63 + X64 + X65 <= 1 108) X52 + X61 + X62 + X63 + X64 + X65 + X66 <= 1 109) X53 + X61 + X62 + X63 + X64 + X65 + X66 + X67 <= 1 110) X54 + X61 + X62 + X63 + X64 + X65 + X66 + X67 + X68 <= 1 111) X55 + X61 + X62 + X63 + X64 + X65 + X66 + X67 + X68 + X69 <= 1 112) X56 + X62 + X63 + X64 + X65 + X66 + X67 + X68 + X69 + X610 <= 1 113) X57 + X63 + X64 + X65 + X66 + X67 + X68 + X69 + X610 <= 1 114) X58 + X64 + X65 + X66 + X67 + X68 + X69 + X610 <= 1 115) X59 + X65 + X66 + X67 + X68 + X69 + X610 <= 1 116) X510 + X66 + X67 + X68 + X69 + X610 <= 1 117) X71 + X61 + X62 + X63 + X64 + X65 <= 1 118) X72 + X61 + X62 + X63 + X64 + X65 + X66 <= 1 119) X73 + X61 + X62 + X63 + X64 + X65 + X66 + X67 <= 1 120) X74 + X61 + X62 + X63 + X64 + X65 + X66 + X67 + X68 <= 1 121) X75 + X61 + X62 + X63 + X64 + X65 + X66 + X67 + X68 + X69 <= 1 122) X76 + X62 + X63 + X64 + X65 + X66 + X67 + X68 + X69 + X610 <= 1 123) X77 + X63 + X64 + X65 + X66 + X67 + X68 + X69 + X610 <= 1 124) X78 + X64 + X65 + X66 + X67 + X68 + X69 + X610 <= 1 125) X79 + X65 + X66 + X67 + X68 + X69 + X610 <= 1 126) X710 + X66 + X67 + X68 + X69 + X610 <= 1 127) X191 + X201 + X202 + X203 + X204 + X205 + X181 + X182 + X183 + X184 + X185 <= 2 128) X192 + X201 + X202 + X203 + X204 + X205 + X206 + X181 + X182 + X183 + X184 + X185 + X186 <= 2 129) X193 + X201 + X202 + X203 + X204 + X205 + X206 + X207 + X181 + X182 + X183 + X184 + X185 + X186 + X187 <= 2 130) X194 + X201 + X202 + X203 + X204 + X205 + X206 + X207 + X208 + X181 + X182 + X183 + X184 + X185 + X186 + X187 + X188 <= 2 131) X195 + X201 + X202 + X203 + X204 + X205 + X206 + X207 + X208 + X209 + X181 + X182 + X183 + X184 + X185 + X186 + X187 + X188 + X189 <= 2 132) X196 + X202 + X203 + X204 + X205 + X206 + X207 + X208 + X209 + X2010 + X182 + X183 + X184 + X185 + X186 + X187 + X188 + X189 + X1810 <= 2 133) X197 + X203 + X204 + X205 + X206 + X207 + X208 + X209 + X2010 + X183 + X184 + X185 + X186 + X187 + X188 + X189 + X1810 <= 2 134) X198 + X204 + X205 + X206 + X207 + X208 + X209 + X2010 + X184 + X185 + X186 + X187 + X188 + X189 + X1810 <= 2 135) X199 + X205 + X206 + X207 + X208 + X209 + X2010 + X185 + X186 + X187 + X188 + X189 + X1810 <= 2 136) X1910 + X206 + X207 + X208 + X209 + X2010 + X186 + X187 + X188 + X189 + X1810 <= 2 end