Question 1193939: A farmer is going to divide her 60 acre farm between two crops. Seed for crop A costs $20 per acre. Seed for crop B costs $40 per acre. The farmer can spend at most $1400 on seed.
If crop B brings in a profit of $270 per acre, and crop A brings in a profit of $120 per acre, how many acres of each crop should the farmer plant to maximize her profit?
Answer by ikleyn(52782)   (Show Source):
You can put this solution on YOUR website! .
A farmer is going to divide her 60 acre farm between two crops.
Seed for crop A costs $20 per acre. Seed for crop B costs $40 per acre. The farmer can spend at most $1400 on seed.
If crop B brings in a profit of $270 per acre, and crop A brings in a profit of $120 per acre,
how many acres of each crop should the farmer plant to maximize her profit?
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Seed for crop B is twice as expensive as seed for crop A, but gives the profit which is more than twice as big
as the profit of crop A (compare 270/120 = 2.25 with 40/20 = 2 !).
+---------------------------------------------------------------+
| THEREFORE, it is clear, that the most aggressive strategy |
| is to sow as much area with crop B as possible. |
+---------------------------------------------------------------+
The possible area to sow with crop B, within the budget, is 1400/40 = 35 acres.
So, the most profitable solution is to sow 35 acres with crop B and do not sow crop A, at all.
The expected profit is then 35*270 = 9450 dollars, and it is maximal possible profit at given conditions.
Solved.
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