Question 1118477: A farmer is going to divide her 40 acre farm between two crops. Seed for crop A costs $10 per acre. Seed for crop B costs $20 per acre. The farmer can spend at most $500 on seed. If crop B brings in a profit of $40 per acre, and crop A brings in a profit of $110 per acre, how many acres of each crop should the farmer plant to maximize her profit?
____ acres of crop A
____ acres of crop B
Found 2 solutions by stanbon, Alan3354:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A farmer is going to divide her 40 acre farm between two crops. Seed for crop A costs $10 per acre. Seed for crop B costs $20 per acre. The farmer can spend at most $500 on seed. If crop B brings in a profit of $40 per acre, and crop A brings in a profit of $110 per acre, how many acres of each crop should the farmer plant to maximize her profit?
Inequalities::
Acres:: A + B <= 40
Seed:: 10A + 20B <= 500
Profit function:: P = 110A + 40B
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Rearrange Inequalities::
0<= A <=40
0<= B <= 40
A <= -B + 40
A <= -2B + 50
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Graph in the 1st Quadrant::
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Find the points of intersection:(0,40),(10,30),(25,0)
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Find maximum-profit coordinates:: (B,A)
Profit = 110A + 40B
Using (0,40):: P = 110*40 + 40*0 = $4400
Using (10,30): P = 110*30+40*10 = $3300+400 = $3700
Using (25,0):: P = 110*0+40*25 = 0 + $1000 = $1000
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40____ acres of crop A
0____ acres of crop B
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Cheers,
Stan H.
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Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! A farmer is going to divide her 40 acre farm between two crops. Seed for crop A costs $10 per acre. Seed for crop B costs $20 per acre. The farmer can spend at most $500 on seed. If crop B brings in a profit of $40 per acre, and crop A brings in a profit of $110 per acre, how many acres of each crop should the farmer plant to maximize her profit?
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____ acres of crop A
____ acres of crop B
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Don't type that. It's a waste of time, and it's irritating.
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Since the profit per acre is given, the cost of seeds is not relevant.
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crop A = all 40 acres
cost = 40*10 = $400
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---> crop B = 0 acres
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