A farmer has 10 acres of land to grow soy beans or corn and he can...

 

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A farmer has 10 acres of land to grow soy beans or corn and he can spend a maximum of 1200 CHF on seeds. Since the weather is forecasted to change, the planting needs to be done within the next 12 hours. The farmer chooses the mix of crops to maximize profits and he wants to achieve profits of at least 1500 CHF to start operating. The table summarizes some figures on the two crops. Soy Beans Sweet Corn Price of seeds Seeds per acre [CHF/kg] [kg/acre] 5 40 2 50 Sowing time Profit per acre [h/acre] [CHF/acre] 1 500 2 300 (a) State the farmer's LP problem in canonical and standard form. (b) Determine the feasible region graphically. (c) Find the optimal mix of crops graphically. (d) Are there any redundant constraints? (e) Perform a sensitivity analysis: What is the range of profits per acre of soy beans for which the optimal solution is stable? Compute all critical values of the profit per acre for soy beans. (f) Determine the value of the slack variables. (g) Are the shadow prices non-zero? What is the economic meaning of the shadow prices on the binding (tight) constraints? (h) Implement the model in canonical form in GAMS. Verify your results from (c), (f) and (g) with the help of your GAMS model. A farmer has 10 acres of land to grow soy beans or corn and he can spend a maximum of 1200 CHF on seeds. Since the weather is forecasted to change, the planting needs to be done within the next 12 hours. The farmer chooses the mix of crops to maximize profits and he wants to achieve profits of at least 1500 CHF to start operating. The table summarizes some figures on the two crops. Soy Beans Sweet Corn Price of seeds Seeds per acre [CHF/kg] [kg/acre] 5 40 2 50 Sowing time Profit per acre [h/acre] [CHF/acre] 1 500 2 300 (a) State the farmer's LP problem in canonical and standard form. (b) Determine the feasible region graphically. (c) Find the optimal mix of crops graphically. (d) Are there any redundant constraints? (e) Perform a sensitivity analysis: What is the range of profits per acre of soy beans for which the optimal solution is stable? Compute all critical values of the profit per acre for soy beans. (f) Determine the value of the slack variables. (g) Are the shadow prices non-zero? What is the economic meaning of the shadow prices on the binding (tight) constraints? (h) Implement the model in canonical form in GAMS. Verify your results from (c), (f) and (g) with the help of your GAMS model.

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