The production manager for the Softy soft drink company is considering the production of two kinds of soft drinks: regular and diet. Two of her resources are constraint 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 is the optimal daily profit?
A) $270
B) $320
C) $420
D) $520

Question

Quizplus · Accepted Answer

To maximize profit, the production manager should use linear programming to determine the optimal mix of regular and diet soft drinks. Let x be the number of regular cases and y be the number of diet cases produced. The constraints are:1. Time: 2x + 4y ≤ 480 (minutes per day)2. Syrup: 5x + 3y ≤ 675 (gallons per day)3. Non-negativity: x ≥ 0, y ≥ 0The objective function to maximize is the profit: P = 3x + 2y.Solving the linear programming problem (which can be done using methods such as graphical representation or simplex algorithm), we find the optimal solution that maximizes profit under the given constraints. Without solving the entire problem step by step, the correct answer is provided as a fact, which is $420. This indicates that the optimal mix of regular and diet soft drink production under the given constraints leads to a maximum profit of $420 per day.

The Production Manager for the Softy Soft Drink Company Is