Question

A farmer is creating a budget for planting soybeans and wheat. Planting soybeans costs $200 per acre and planting wheat costs $500 per acre. He wants to spend no more than $100,000 planting soybeans and wheat. What is the "multiplier" for soybeans? ​

Answer 1

The multiplier for soybeans is 200, which is dollars per acre.

Explanation:

5 acres ≤ soybeans ≤ 495 acres (constraint)

2 acres ≤ wheat ≤ 198 acres (constraint)

150w + 125s = 100,000

This would represent 150 acres of wheat and 125 acres of soybeans. The acres of wheat would add up to $75,000 because 150 x 500 = 75,000 and the acres of soybeans would add up to $25,000 because 125 x 200 = 25,000. (example of a solution, there are more possible)

Answer 2

5 acres < soybeans < 495

2 acres < wheat < 198 acres

Explanation:

If farmer plans to plant minimum of soybeans, it should be 5 acres of soybeans costing $1000. The remaining cost of $98,000 will be available for maximum of wheat, i.e., 198 acres of wheat.

Similarly, if we go for minimum possible planting for wheat, it should be 2 acres, and then resulting in 495 acres for soybeans

5 acres < soyabeans < 495

2 acres < wheat < 198 acres