Art Kumar lives on the outskirts of Draper and has a Iacre l

Art Kumar lives on the outskirts of Draper and has a I-acre lot nex t to his home. He plans
to grow vegetables on the lot and sell them at the downtown market during the summer. He
doesn\'t have enough time to grow the vegetables himself so he has hired a local college student
to plant and tend the garden and sell the crops at the market. Art is considering five vegetables
to pl ant that seem to be popul ar at the market-asparagus, corn, tomatoes, green beans, and
red peppers. Art estimates the fo llowing yields per acre for each vegetable-2,000 pounds of
asparagus, 7,200 pounds of corn, 25,000 pounds of tomatoes, 3,900 pounds of green beans, and
12,500 pounds of red peppers. The costs per acre are $ 1,800 for asparagus, $ 1,740 for corn,
$6,000 for tomatoes, $3,000 for green beans, and $2,700 fo r red peppers. Asparagus sells for
$ 1.90 per pound, corn sells for $0.10 per pound, tomatoes sell for $3.25 per pound, green beans
sell for $3 .40 per pound, and red peppers sell for $3.45 per pound. He has budgeted $5,000 for
the garden. Talking to some of the other market vendors, he estimates that he will not sell more
than 1,200 pounds of asparagus, 10,000 pounds of tomatoes, 2,000 pounds of green beans, and
5,000 pounds of red peppers. Art wants to know the portion of his lot that he should plant with
each vegetable in order to maximize his revenue.
a. Formul ate a linear programming model for this problem
b. Solve the model by using the computer.

Solution

A.Let the Asparagus be a

Let the  corn be b

Let the tomatoes be c

Let the green beans be d

Let the red peppers be e

2000a+7200b+25000c+3900d+12500e=1
1800a+1740b+6000c+3000d+2700e=5000

B.Linear programming model using computer

a=450

b=1000

c=1500

d=2500

e=2000