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A farmer has a 40-acre farm in Georgia. The farmer is trying to determine how many...

A farmer has a 40-acre farm in Georgia. The farmer is trying to determine how many acres of corn, peanuts, and cotton to plant. Each crop requires labor, fertilizer, and insecticide. The farmer has developed the following linear programming model to determine the number of acres of corn (x1), peanuts (x2), and cotton (x3) to plant in order to maximize profit.

Max400(X1) + 350(X2) + 450(X3)

s.t.

Constraint 1: 2(x1) + 3(X2) + 2(X3) 120labor hours

Constraint 2: 4(x1) + 3(X2) + 1(X3) 120fertilizer, tons

Constraint 3: 3(x1) + 2(X2) + 4(X3) 100insecticide, tons

Constraint 4:(x1) + (X2) + (X3) 40acres

(x1), (X2), (X3) 0

1.Which constraints are binding?

2.How many acres of corn should be planted?

3.how many acres of cotton acres should be planted?

4.how many acres of peanuts acres should be planted?

5.what is the maximum profit?

6.How much profit will increase if you can get 10 more tons of insecticide?

Math   Statistics-And-Probability   
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