A forestry company needs to control insects which can damage the trees. Traditionally, this meant aerial...

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A forestry company needs to control insects which can damage the trees. Traditionally, this meant aerial spraying of insecticide. However, the company was concerned about the effects of this insecticide on the environment and on the health of their workers, and they were investigating other ways to control the insects. There are two competing environmentally-friendly technologies. Technology 1 costs $200 per hectare, while Technology 2 costs $250 per hectare. The forestry company wants at least 35,000 hectares of land to be protected from insects. For this year, supply chain restrictions have limited the use of Technology 1 at this location to 18,000 hectares, and Technology 2 is limited to 25,000 hectares. Both technologies require water. Though essentially free, it is in limited supply. Technology 1 requires 4 cubic metres per hectare, and Technology 2 requires 3 cubic metres per hectare. There are 150,000 cubic metres of water available. (a) Using variables named X1 and X2, formulate a linear optimization model for this situation. Write every constraint in standard form (≤, =, or ≥ a number), with a one or two word description of the purpose of the constraint. (b) Using only the 30,000 by 30,000 space as provided on the graph paper shown below, plot the constraint boundaries (with word description next to it) with arrows to show the direction of the inequality, show the feasible region, the trial and optimal isovalue lines, and the point of optimality. Compute the exact solution algebraically, and clearly state the recommendation and the OFV. A forestry company needs to control insects which can damage the trees. Traditionally, this meant aerial spraying of insecticide. However, the company was concerned about the effects of this insecticide on the environment and on the health of their workers, and they were investigating other ways to control the insects. There are two competing environmentally-friendly technologies. Technology 1 costs $200 per hectare, while Technology 2 costs $250 per hectare. The forestry company wants at least 35,000 hectares of land to be protected from insects. For this year, supply chain restrictions have limited the use of Technology 1 at this location to 18,000 hectares, and Technology 2 is limited to 25,000 hectares. Both technologies require water. Though essentially free, it is in limited supply. Technology 1 requires 4 cubic metres per hectare, and Technology 2 requires 3 cubic metres per hectare. There are 150,000 cubic metres of water available. (a) Using variables named X1 and X2, formulate a linear optimization model for this situation. Write every constraint in standard form (≤, =, or ≥ a number), with a one or two word description of the purpose of the constraint. (b) Using only the 30,000 by 30,000 space as provided on the graph paper shown below, plot the constraint boundaries (with word description next to it) with arrows to show the direction of the inequality, show the feasible region, the trial and optimal isovalue lines, and the point of optimality. Compute the exact solution algebraically, and clearly state the recommendation and the OFV.