The production planner for Fine Coffees, Inc. produces two coffee blends: American (A) and British (B). He can only get 300 pounds of Colombian beans per week and 200 pounds of Dominican beans 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 weekly profit when producing the optimal amounts?
A)$0.
B)$400.
C)$700.
D)$800.
E)$900.

Question

Quizplus · Accepted Answer

To find the optimal amounts of each blend to produce, we can set up a linear programming problem. Let x be the number of pounds of American blend coffee produced, and let y be the number of pounds of British blend coffee produced. Then we want to maximize the weekly profit Z:

Z = 2x + y

subject to the constraints:

12x + 8y ≤ 300 (constraint on Colombian beans)
4x + 8y ≤ 200 (constraint on Dominican beans)
x ≥ 0, y ≥ 0 (non-negativity constraints)

We can graph the feasible region determined by these constraints and find the corner points:

(0, 25), (16.67, 16.67), (25, 0)

If we plug in each of these points into the profit function, we get:

(0, 25): Z = 1(25) = 25
(16.67, 16.67): Z = 2(16.67) + 1(16.67) = 50.01
(25, 0): Z = 2(25) = 50

So the optimal amounts are to produce 16.67 pounds of American blend coffee and 16.67 pounds of British blend coffee, for a total weekly profit of $50.01.

The Production Planner for Fine Coffees, Inc