The production manager for the Coory soft drink company is considering the produ
ID: 3035450 • Letter: T
Question
The production manager for the Coory soft drink company is considering the production of two kinds of soft drinks: regular and diet. Two of her limited resources are 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 $2.00 per case. What are the optimal daily production quantities of each product and the optimal daily profit? Can someone please write out the way to solve the optimal solution? Not using excel.
Explanation / Answer
Let X denote regular and Y denotes diet
Given information is
Objectve Function:
Max Z = 3X + 2Y
Subject to constraints
2X + 4Y 480 minutes
5X + 3Y 675
Profit = 3X + 2Y
480 minutes allows us to produce 240 regular cases or 120 diet cases. But we can only produce 675/5 = 135 regular cases or 675/3 = 225 diet cases a day
But to see that all the constraints are satisfies, we have to find a feasible region of all the constrains
We can try and find the intersection of these constraints
2X + 4Y 480
5X + 3Y 675
By solving these two equations we will see that X = 90, Y = 75
Optimal profit = 90*3 + 75*2 = 420$
Production Time Syrup regular 2 5 Diet 4 3 Total 480 675Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.