Question

A chicken farm orders bags of feed from two farmers. Store X charges $20 per bag, and store Y charges $15 per bag. The farm must obtain at least 60 bags per week to care for the chickens properly. Store Y can provide a maximum of 40 bags per week, and the farm has committed to buy at least as many bags from store X as from store Y. The chicken farm wants to minimize the cost of ordering feed. Let x represent the number of bags of feed from store X and y represent the number of bags of feed from store Y. What are the constraints for the problem?

Answer 1

x + y ≥ 60;

y ≤ 40;

x ≥ y;

x ≥ 0, y ≥ 0

Explanation:

Here x represents the number of bags of feed from store X and y represents the number of bags of feed from store Y.

Given,

The farm must obtain at least 60 bags per week to care for the chickens properly,

⇒ x + y ≥ 60,

Also, Store Y can provide a maximum of 40 bags per week, and the farm has committed to buy at least as many bags from store X as from store Y.

⇒ y ≤ 40 and x ≥ y,

Now, the number of bags can not be negative,

⇒ x ≥ 0 and y ≥ 0,

Hence, the constraints for the given problem are,

x + y ≥ 60;

y ≤ 40;

x ≥ y;

x ≥ 0, y ≥ 0