Question 504498: Formulate but do not solve the following exercise as a linear programming problem.
A farmer plans to plant two crops, A and B . The cost of cultivating crop A is $40/acre whereas that of crop B is $70/acre. The farmer has a maximum of $7710 available for land cultivation. Each acre of crop A requires 20 labor-hours, and each acre of crop B requires 24 labor-hours. The farmer has a maximum of 3008 labor-hours available. If she expects to make a profit of $190/acre on crop A and $200/acre on crop B, how many acres of each crop, x and y, respectively, should she plant in order to maximize her profit, P?
P = ? subject to the constraints
cost ?
labor ?
x ≥ 0
y ≥ 0
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A farmer plans to plant two crops, A and B .
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A>= 0
B>= 0
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The cost of cultivating crop A is $40/acre whereas that of crop B is $70/acre.
The farmer has a maximum of $7710 available for land cultivation.
Cost: 40A + 70B <= 7710
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Each acre of crop A requires 20 labor-hours, and each acre of crop B requires 24 labor-hours. The farmer has a maximum of 3008 labor-hours available.
Labor: 20A + 24B <= 3008
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If she expects to make a profit of $190/acre on crop A and $200/acre on crop B, how many acres of each crop, x and y, respectively, should she plant in order to maximize her profit, P?
Objective Function: P = 190A + 200B
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Cheers,
Stan H.
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