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# objective function

There are two questions:

The production manager for the Whoppy soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. The company operates one "8 hour" shift per day. Therefore, the production time is 480 minutes per day. During the production process, one of the main ingredients, syrup is limited to maximum production capacity of 675 gallons per day. Production of a regular case requires 2 minutes and 5 gallons of syrup, while production of 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. How many cases of regular and how many cases of diet soft drink should Whoppy produce to maximize daily profit?

Formulate the objective function
Formulate the constraint for Time
Formulate the constraint for Syrup
What is the optimal solution?
Use QM to solve.

From the above problem, if the company decides to increase the amount of syrup it uses during production of these soft drinks to 990lbs. will the current product mix change? How many cases of each type of soft drink should the company producer? How much will profit increase?

Use QM to solve the new problem.