A farmer must decide how to allocate his 101 acres of land between com, oats and

Question

A farmer must decide how to allocate his 101 acres of land between com, oats and wheat. It takes 1.9 hours per acre to harvest corn, 2.3 hours per acre to harvest oats and 3.3 hours per acre to harvest wheat. He can work up to 221 on the harvest. Additionally, his water supply is limited to 520000 gallons per day and it takes 5090, 5290 and 5570 gallons per day at their peak to water an acre of corn, oats and wheat, respectively. Each acre of corn generates $22 in profit, each acre of oats generates $25 and each acre of wheat generates $29. If the wants to manage whole (not decimal/fractional) acres, what is the optimal allocation? (You may use Solver, provide integer values) Corn Oat Wheat What is the farmer's profit under this allocation $ week

Explanation / Answer

Ans:

Let X1 be the allocation to corn

X2 be the allocation to oats

X3 be tha allocation to wheat

subject to

Solved using simplex method(solver):

The optimal solution value is Z = 2424.08
X1 = 16.25
X2 = 82.66
X3 = 0

But if farmer wants to use all land then allocate:

X1=17

X2=83

X3=1

(Note:plz try near about approximate options)

Farmer's profit=22*17+25*83+29*1=2478

MAXIMIZE: 22 X1 + 25 X2 + 29 X3

subject to

5090 X1 + 5290 X2 + 5570 X3 520000
1.9 X1 + 2.3 X2 + 3.3 X3 221
1 X1 + 1 X2 + 1 X3 101

X1, X2, X3 0

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