A chicken farm orders bags of feed from two stores. Store cap x charges 20 dollars per bag, and store cap y charges 15 dollars per bag. The farm must obtain at least 60 bags per week to care for the chickens properly. Store cap y can provide a maximum of 40 bags per week, and the farm has committed to buy at least as many bags from store cap x as from store cap y The chicken farm wants to minimize the cost of ordering feed. Let x represent the number of bags of feed from store cap x and y represent the number of bags of feed from store cap y What are the constraints for the problem?
Answer
A
20 x plus 15 y is greater than or equal to 60 x is greater than or equal to y y is less than or equal to 40 x is greater than or equal to 0 y is greater than or equal to 0
B
x plus y is greater than or equal to 60 x is greater than or equal to y y is less than or equal to 40 x is greater than or equal to 0 y is greater than or equal to 0
C
x plus y is less than or equal to 60 x is greater than or equal to y y is less than or equal to 40 x is greater than or equal to 0 y is greater than or equal to 0
D
x plus y is greater than or equal to 60 y is greater than or equal to x y is less than or equal to 40 x is greater than or equal to 0 y is greater than or equal to 0
Explanation
The farm needs at least 60 bags total, so x + y ≥ 60. It must buy at least as many bags from store x as from store y, so x ≥ y, and store y’s limit gives y ≤ 40. The numbers of bags cannot be negative, so x ≥ 0 and y ≥ 0. These are the constraints in choice B; the prices belong in the cost function, not the total-bag constraint.
AI-written and checked against the verified answer.