SOLUTION: A farmer is going to divide her 60 acre farm between two crops. Seed for crop A costs $25 per acre. Seed for crop B costs $50 per acre. The farmer can spend at most $2500 on seed.

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Question 1198870: A farmer is going to divide her 60 acre farm between two crops. Seed for crop A costs $25 per acre. Seed for crop B costs $50 per acre. The farmer can spend at most $2500 on seed. If crop B brings in a profit of $80 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=

Answer by ikleyn(52781) About Me  (Show Source):
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A farmer is going to divide her 60 acre farm between two crops.
Seed for crop A costs $25 per acre. Seed for crop B costs $50 per acre.
The farmer can spend at most $2500 on seed.
If crop B brings in a profit of $80 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?
~~~~~~~~~~~~~~ 

Seed for crop A ($25 per acre) are cheaper than seed for crop B ($50 per acre).

At the same time, profit of crop A ($110 per acre) is greater than profit
of crop B ($50 per acre).


The common sense says that the winning strategy is to use as many acres 
for crop A as possible.


So, divide $2500 by $25 to estimate possible area for crop A

    2500%2F25 = 100 acres.


Thus, there are enough money for seed A for 60 acres.


So, the optimal strategy is to cultivate crop A only on all 60 acres.


It will give a profit of 60*110 = 6600 dollars.

Solved.