A farmer must decide how to allocate his 103 acres of land between corn, oats an

Question

A farmer must decide how to allocate his 103 acres of land between corn, oats and wheat. It takes 1.8 hours per acre to harvest corn, 2.7 hours per acre to harvest oats and 1.6 hours per acre to harvest wheat. He can work up to 231 on the harvest. Additionally his water supply is limited to 520000 gallons per day and it takes 5090 and 5970 gallons per day at their peak to water an acre of corn, oats and wheat, respectively. Each acre of corn generates $34 in profit, each acre of oats generates $31 and each acre of wheat generates $20. What is the optimal allocation? (you may use solver, round to two decimal places as needed) Corn Oat Wheat What is the farmer's profit under this allocation $/(Round to two decimal places as needed) How much more would be pay for an additional 1000 gallons/day? $ (Round to two decimal places as needed).

Explanation / Answer

Ans:

Let

X1 be allocated to Corn

X2 be allocated to Oats

X3 be allocated to Wheat

subject to

The optimal solution value is Z = 3473.48
X1 = 102.16
X2 = 0
X3 = 0

Hence,Corn should be alocated all of the acres i.e. 103 acres

Profit of farmer=3502

MAXIMIZE: 34 X1 + 31 X2 + 20 X3

subject to

1.8 X1 + 2.7 X2 + 1.6 X3 231
5090 X1 + 5680 X2 + 5970 X3 520000
1 X1 + 1 X2 + 1 X3 103
X1, X2, X3 0

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