Question: Formulate a linear program that maximises the net present value (NPV) of the forestland. Explain your model! (Hint: Define decision variable xi,j to reflect the number of km2 in analysis area i, managed according to plan j)

The Forest Service manages 788 km2 of forestland, that is divided into seven homogeneous analysis areas. Three management plans are drawn for each area encouraging timbering, grazing and wilderness preservation respectively as shown in the following table. The Forest Service seeks to maximise the Net Present Value (NPV) while producing at least 40 thousand units of timber, at least 5 animal unit months of grazing, and keeping an average wilderness index to at least 70.

Area ID km. Plan NPV ( per km) Timber (per km) Grazing (per km) Wilderness Index 1 75 1 503 310 0.01 2 140 50 0.04 80 8 8 8 8 3 203 0 0 N 2 90 1 675 198 0.03 2 100 48 0.08 60 3 45 0 0 65 3 140 1 630 210 0.04 45 2 105 57 0.07 55 3 40 0 0 60 4 4 80 1 330 112 0.01 30 2 40 30 0.02 35 3 3 295 0 0 90 5 212 1 105 40 0.05 80 2 480 32 0.08 60 ~ 3 120 0 0 0 70 6 98 490 105 0.02 35 2 55 25 0.03 50 3 180 0 0 0 75 7 113 1 705 213 0.02 40 2 60 40 0.04 45 3 400 0 0 95