HELP PLEASE ASAP

Question

A farmer is going to divide her 50 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 $1500 on seed.

If crop B brings in a profit of $270 per acre, and crop A brings in a profit of $140 per acre, how many acres of each crop should the farmer plant to maximize her profit? how many acres does of crop A and B have

Answer 1

Hey Alaina!

The key to this tricky question is to think about the definition of profit! Profit = Revenue (how much money the farmer will make) - Cost (how much the farmer paid for the seed).

Therefore:

-Planting 1 acre of crop B will lead to: profit = $270-$50 = $220

-Planting 1 acre of crop A will lead to: profit = $140-$25 = $115

-The farmer will profit $105 more for every acre they plant crop B than they will for crop A

We know the farmer can spend $1500 on seed, so $1500/$50=30 acres of crop B to maximize their profit.

However, this plan would leave 20 acres of the land unused. If the farmer wanted to utilize all of the land regardless of profit, they would spend $1000 for 40 acres of crop A and $500 for 10 acres of crop B to use all 50 acres of land. This would of course not profit as much as only planting crop B.

Hope this is helpful!