A farmer owns 135 acre farm and plans to plant at most three crops. The seed for

Question

A farmer owns 135 acre farm and plans to plant at most three crops. The seed for crops A,B and C cost $24, $45 and $30 per acre, respectively. A maximum of $3,870 can be spend on seed. Crops A,B and C require 1, 2 and 2 work days per acre, respectively and there are a mx of 180 workdays available. if the farmer can make a profit of $140 per acre on crop A, $200 per acre on crop B, and $160 on crop C, how man acres of each crop should be planted to maximize profit? The farmer should plant ___ acres of crop A, ___ acres of crop B, and ____ acres of crop C, for a profit of $_____

Explanation / Answer

Are you getting paid by the hour? I think you're missing some information. You are trying to maximize something....farming profit, etc? Maybe you're just trying to keep busy the whole time available? I'll assume the latter. Then you have two equations in to variables. let s = acres of soybeans let c = acres of corn 6s + 8c = 660 s + c = 100 Multiply the second equation by 6 6s + 8c = 660 6s + 6c = 600 -------------------- 2c = 60 (subtracting the second equation from the first) c = 30 => s = 70

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