A farmer has 300 acres of available land and $60,000 to spend. He wants to plant

Question

A farmer has 300 acres of available land and $60,000 to spend. He wants to plant the combination of crops which maximizes his profit. Complete parts a. through c. below Profits and Constraints for Crops Potatoes Com r of Acres (per acre) (per acre) x3 S224 $30- Total 300 $60,000 S320 S60 $128 $20 a. Give the dual problem. subject to |y1 + 320g 60 y1 +128y2! 120 y1 +224Y2| 130 y120, y2z0 with b. The solution to the dual problem can be interpreted as shadow profits. Use shadow profits to estimate the farmer's profit if land is cut to 270 acres but capital increases to $63,000 The farmer's estimated profit is c. Suppose the farmer has 330 acres of land but only $57,000. Find the optimum profit and the planting strategy that will produce this profit. Planting acres of potatoes acres of corn, and acres of cabbage will produce an optimal profit of $

Explanation / Answer

a)

min Z = 300y1 = 60000y2
y1 + 320 y2 >=60
y1 + 128y2 >= 20
y1 + 224y2 >=30
y1, y2 >=0

b) Profit : 10362.50

c) 20 acres of potatoes, 0 acres of com and 0 accres of cabbage will produce an optimual profit of $10362,.50

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