goal programming

A Company manages three sites of forestlandfor timber production and reforestation with the respective areas of 100,000,180,000, and 200,000 acres. The main timber products include three categories: pulpwood, plywood, and sawlogs. Several reforestation alternatives are availablefor each site, each with its cost, number of rotation years (i.e., number of years from seedling size until harvesting), return from rent, and production output. The following table summarizes this information. Annual $/acre Rotation Annual m/acre Site 1 Sawlogs 0 0 800 Rent 160 117 140 195 182 DOO Pulpwood Plywood 12 0 10 0 5 6 4 7 3 2 3 0 9 0 8 0 5 A6 180 A7 2 Alternative cost A1 1000 A2 A3 1500 A4 1200 A5 1300 1200 1500 A1 1000 A2 800 A3 1500 A4 1200 AS 1300 A6 1200 A1 1000 A2 800 A3 1500 A4 1200 A5 1300 yr 20 25 40 15 40 40 50 20 25 40 15 40 40 20 25 40 15 40 135 102 55 95 120 100 90 60 48 60 65 35 NNNNWN DOWNWER 4 0 0 0 4 3 5 4 0 0 4 3 5 0 0 0 1 To guarantee sustained future production, each acre of reforestation in each alternative requires that as many acres as years in rotation be assigned to that alternative. The rent column represents the stumpage value per acre. The goals of Warehouzer are: 1. Annual outputs of pulpwood, plywood, and saw logs are 200,000, 150,000, and 350,000 cubic meters, respectively. 2. Annual reforestation budget is $2.5 million. 3. Annual return from land rent is $100 per acre. How much land at each site should be assigned to each alternative? A Company manages three sites of forestlandfor timber production and reforestation with the respective areas of 100,000,180,000, and 200,000 acres. The main timber products include three categories: pulpwood, plywood, and sawlogs. Several reforestation alternatives are availablefor each site, each with its cost, number of rotation years (i.e., number of years from seedling size until harvesting), return from rent, and production output. The following table summarizes this information. Annual $/acre Rotation Annual m/acre Site 1 Sawlogs 0 0 800 Rent 160 117 140 195 182 DOO Pulpwood Plywood 12 0 10 0 5 6 4 7 3 2 3 0 9 0 8 0 5 A6 180 A7 2 Alternative cost A1 1000 A2 A3 1500 A4 1200 A5 1300 1200 1500 A1 1000 A2 800 A3 1500 A4 1200 AS 1300 A6 1200 A1 1000 A2 800 A3 1500 A4 1200 A5 1300 yr 20 25 40 15 40 40 50 20 25 40 15 40 40 20 25 40 15 40 135 102 55 95 120 100 90 60 48 60 65 35 NNNNWN DOWNWER 4 0 0 0 4 3 5 4 0 0 4 3 5 0 0 0 1 To guarantee sustained future production, each acre of reforestation in each alternative requires that as many acres as years in rotation be assigned to that alternative. The rent column represents the stumpage value per acre. The goals of Warehouzer are: 1. Annual outputs of pulpwood, plywood, and saw logs are 200,000, 150,000, and 350,000 cubic meters, respectively. 2. Annual reforestation budget is $2.5 million. 3. Annual return from land rent is $100 per acre. How much land at each site should be assigned to each alternative