Question 202987: A fruit grower has 150 acres of land available to raise two crops, A and B. It takes 1 day to trim an acre of crop A and 2 days to trim an acre of crop B, and there are 240 days available each year for trimming. It takes 0.3 days to pick an acre of crop A and 0.1 days to pick an acre of crop B, and there are 30 days per year available for picking. The profit is $140 per acre for crop A and $235 per acre for crop B. Determine the optimal acreage for each fruit and the optimal profit. (Show all your work including any graphs you used.)
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! : A fruit grower has 150 acres of land available to raise two crops, A and B.
It takes 1 day to trim an acre of crop A and 2 days to trim an acre of crop B,
and there are 240 days available each year for trimming.
It takes 0.3 days to pick an acre of crop A and 0.1 days to pick an acre of crop B,
and there are 30 days per year available for picking.
The profit is $140 per acre for crop A and $235 per acre for crop B.
Determine the optimal acreage for each fruit and the optimal profit.
(Show all your work including any graphs you used.)
:
Write an equation for each statement, rearrange for graphing:
:
" A fruit grower has 150 acres of land available to raise two crops, A and B."
A + B = 150
A = 150-B; (red)
:
It takes 1 day to trim an acre of crop A and 2 days to trim an acre of crop B,
and there are 240 days available each year for trimming."
1A + 2B = 240
A =< 240-2B; (green)
:
It takes 0.3 days to pick an acre of crop A and 0.1 days to pick an acre of crop B,
and there are 30 days per year available for picking."
.3A + .1B = 30
.3A = 30 - .1B
A =< 100 - B; (blue)
:
Graph these 3 equations, A on the y axis, B on the x axis
:
The corner points of the area of feasibility:
1. A=100,B=0
2. A=75, B=75
3. A=60,B=90
4. A=0, B=120
:
The profit is $140 per acre for crop A and $235 per acre for crop B.
Find the values of these points:
1. 140(100) + 235(0) = $14,000
2. 140(75) + 235(75) = $28,125
3. 140(60) + 235(90) = $29,550
4. 140(0) + 235(120) = $28,200
:
Plant 60 acres of Plant A, and 90 acres of Plant B, for max profit
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