\u00a0\u00ab\u00a0A given farm can grow two types of crop : wheat and maize. The area to be cultivated must be determined for each crop, knowing that : The primal linear programme is written as follows :<\/p>\n Maximizing Z = 450\u00d71 + 1000\u00d72 Optimal solution, x1*=0; x2*=40; Z=40000<\/p>\n We determined in the unit that the dual programme is written as follows :<\/p>\n Minimizing Z=50y1 + 2000y2 Write this dual programme and check that the value of the objective function is the same as for the primal programme, and find the relationships between the solutions of the primal programme and that of the dual one.<\/strong><\/p>\n Solution :<\/strong><\/p>\n Download the solution model here :\u00a0dual.zip<\/strong><\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":" Length : around 25 minutes You are now going to write the dual programme of the following base model which you wrote in the GAMS introduction lesson. \u00a0\u00ab\u00a0A given farm can grow two types of crop : wheat and maize. Continue reading Activity 9 : \u00ab Wheat\/maize \u00bb model \u2013 Writing a dual model<\/span>
\nThe objective of the farmer is to maximize his income.
\nWheat yields 450\u20ac per hectare, maize 1000\u20ac.
\nWheat requires 25 hours of labour per hectare and per year, and maize 50 hours.
\nThe farm area is 50 ha and the farmer can work 2000 hours a year.\u00a0\u00bb<\/em><\/p>\n
\nwith \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 x1 + x2\u00a0\u2264\u00a050
\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/em>\u00a025\u00d71 + 50\u00d72\u00a0\u2264\u00a02000
\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/em>\u00a0x1, x2 positive
\nx1 : wheat primal area
\nx2 : maize primal area<\/p>\n
\nwith\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 y1 + 25y2 \u2265 450
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/em>\u00a0y1 + 50 y2 \u2265 1000
\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/em>\u00a0y1, y2 positive
\ny1\u00a0: dual value associated to the land constraint
\ny2\u00a0: dual value associated to the labour constraint<\/p>\n![\"\"](\"http:\/\/www.supagro.fr\/wordpress\/modelecoen\/files\/2018\/11\/backUnit.png\")
<\/a><\/p>\n