A forestry cooperative has been granted a license for a period of 5 years, under a government policy to create jobs in the regions, cutting rights in 10 forest sectors of the Leclerc township located on the outskirts of La Tuque. The cutting right allows the cooperative to distribute the timber harvest over the next 5 years. The forestry equipment at her disposal does not allow her to harvest more than 600 hectares of forest per year. But he will need, to maintain a number of jobs acceptable to governing government authorities, cut at least 200 hectares per year of the forests granted. The later will be the cuts in a sector and more substantial will be the product of these cuts, as evidenced by the following table.

The cooperative wants to maximize the total timber harvest over the life of the concession. When should it exercise its cutting rights in each of the sectors knowing that the a sector cut must be completed in the same year it was started? Formulate the linear programming model using the following variables: Xij = 1 if the cutting right is exercised in sector i during year j Xij = 0 otherwise i = 0, 1,, 9 j = 1, 2, 3, 4, 5

Nombre d'units de bois obtenu dans chaque secteur selon l'anne de la coupe Surface Secteur (en hectares) Anne 1 Anne 2 Anne 3 Anne 4 Anne 5 290 1200 1320 1452 1597 1757 348 1500 1650 1815 1997 2196 210 800 880 968 1065 1171 3 246 975 1073 1180 1298 1427 4 450 495 545 599 659 522 2500 2750 3025 3328 3660 6 506 2400 2640 2904 3194 3514 132 450 495 599 659 8 157 560 616 678 745 820 9 197 740 814 895 985 1083 132 ON MO 000 545 Nombre d'units de bois obtenu dans chaque secteur selon l'anne de la coupe Surface Secteur (en hectares) Anne 1 Anne 2 Anne 3 Anne 4 Anne 5 290 1200 1320 1452 1597 1757 348 1500 1650 1815 1997 2196 210 800 880 968 1065 1171 3 246 975 1073 1180 1298 1427 4 450 495 545 599 659 522 2500 2750 3025 3328 3660 6 506 2400 2640 2904 3194 3514 132 450 495 599 659 8 157 560 616 678 745 820 9 197 740 814 895 985 1083 132 ON MO 000 545