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. Which of the following is not a feasible production combination?
A)0 R and 0 S
B)0 R and 240 S
C)180 R and 120 S
D)300 R and 0 S
E)180 R and 240 S

Question

Quizplus · Accepted Answer

Option E (180 R and 240 S) is not feasible because it exceeds the constraints for both production time and carbonated water. Calculating the requirements for 180 cases of root beer and 240 cases of sassafras soda: Root beer requires 2 minutes per case, so 180 cases would need 360 minutes (or 6 hours), and sassafras soda requires 3 minutes per case, so 240 cases would need 720 minutes (or 12 hours). Together, they would require 18 hours, exceeding the 12-hour time limit. Additionally, both drinks require 5 gallons of water per case, so the total water needed would be (180+240) * 5 = 2100 gallons, exceeding the 1500 gallon limit.

The Production Planner for a Private Label Soft Drink Maker