The production planner for Fine Coffees,Inc.produces two coffee blends: American (A)and British (B).Two of his resources are constrained:
Colombia beans,of which he can get at most 300 pounds (4,800 ounces)per week; and Dominican beans,of which he can get at most 200 pounds (3,200 ounces)per week.Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans; while a pound of British blend coffee uses 8 ounces of each type of bean.Profits for the American blend are $2.00 per pound,and profits for the British blend are $1.00 per pound.What is the Colombian bean constraint?
A) 1 A + 2 B ≤ 4,800
B) 12 A + 8 B ≤ 4,800
C) 2 A + 1 B ≤ 4,800
D) 8 A + 12 B ≤ 4,800
E) 4 A + 8 B ≤ 4,800

Question

Quizplus · Accepted Answer

Let A be the number of pounds of American blend coffee produced per week and B be the number of pounds of British blend coffee produced per week.
The resource constraints are:
12A + 8B ≤ 4,800 (Colombian beans)
4A + 8B ≤ 3,200 (Dominican beans)
The objective function is to maximize profit, which is:
Profit = 2A + 1B
Using linear programming, we can solve for the optimal values of A and B that satisfy the constraints and maximize the profit. The answer is B because it is the only choice with the correct coefficients for the Colombian bean constraint.

The Production Planner for Fine Coffees,Inc