The production manager for the Coory soft drink company is considering the production of two kinds of soft drinks: regular and diet. Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients), limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What are the optimal daily production quantities of each product and the optimal daily profit?
A) R = 75, D = 90, Z = $405
B) R = 135, D = 0, Z = $405
C) R = 90, D = 75, Z = $420
D) R = 40, D= 100, Z = $320

Question

Quizplus · Accepted Answer

Let R be the number of regular cases and D be the number of diet cases produced per day.
The objective function is Z = 3R + 2D (maximize daily profit)
Subject to:
2R + 4D ≤ 480 (production time constraint)
5R + 3D ≤ 675 (syrup constraint)
R, D ≥ 0 (non-negativity constraint)
Solving the above inequalities, we get R = 90 and D = 75, which gives us the optimal daily profit of $420. Therefore, the best choice is (C).

The Production Manager for the Coory Soft Drink Company Is