The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R)and sassafras soda (S). Two resources are constrained: production time (T), of which she has at most 12 hours per day; and carbonated water (W), of which she can get at most 1,500 gallons per day. A case of root beer requires 2 minutes of time and 5 gallons of water to produce, while a case of sassafras soda requires 3 minutes of time and 5 gallons of water. Profits for the root beer are $6.00 per case, and profits for the sassafras soda are $4.00 per case. What are optimal daily profits?
A)$960
B)$1,560
C)$1,800
D)$1,900
E)$2,520

Question

Quizplus · Accepted Answer

To maximize profits, the planner should prioritize the production of the product with the highest profit margin per constrained resource unit. Both products use the same amount of water per case, but root beer has a higher profit ($6) compared to sassafras soda ($4). Therefore, the planner should produce as much root beer as the constraints allow.The time constraint is 12 hours per day, which is 720 minutes (12 hours * 60 minutes/hour). Since a case of root beer requires 2 minutes to produce, the maximum number of root beer cases that can be produced in a day is 720 minutes / 2 minutes/case = 360 cases.The water constraint is 1,500 gallons per day. Since a case of root beer requires 5 gallons of water, the maximum number of root beer cases that can be produced based on the water constraint is 1,500 gallons / 5 gallons/case = 300 cases.The limiting constraint is the water, allowing for the production of 300 cases of root beer. At $6.00 profit per case, the optimal daily profits are 300 cases * $6.00/case = $1,800.

The Production Planner for a Private Label Soft Drink Maker