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). There are at most 12 hours per day of production time and 1500 gallons per day of carbonated water available. 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 is the daily profit when producing the optimal amounts?
A)$960
B)$1,560
C)$1,800
D)$1,900
E)$2,520

Question

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). There are at most 12 hours per day of production time and 1500 gallons per day of carbonated water available. 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 is the daily profit when producing the optimal amounts?
A)$960 
B)$1,560 
C)$1,800 
D)$1,900 
E)$2,520

Quizplus · Accepted Answer

The optimal production is determined by maximizing profit under the constraints of time and water. The constraints are: 2R + 3S ≤ 720 (time in minutes) and 5R + 5S ≤ 1500 (water in gallons). Solving these inequalities, the optimal solution is R = 180 cases and S = 120 cases, resulting in a profit of 6(180) + 4(120) = $1,560.

The Production Planner for a Private Label Soft Drink Maker