The production planner for a private label soft drink maker is planning the prod
ID: 429383 • Letter: T
Question
The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R) and orange soda (S). There are at most 12 hours per day of production time and 1,500 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 orange 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 orange soda are $4.00 per case.
1. Formulate the algebraic version of the appropriate linear programming model for this problem. Make sure to clearly define the decision variables, objective function and all constraints.
2. Using Excel's Solver, find the optimal solution to this problem and report it here (i.e., values of decision variables and of objective function). The optimal solution is actually very intuitive in this case. Can you explain it?
Explanation / Answer
1. Total time availabel per day (in minutes) = 12*60 = 720 hours
let the number of root beer made be R and number of orange soda made be S.
We have to maximize the profit.
Total profit = 6R+4S. This is the objective function that has to be maximized.
Constraints are:
2R+3S<=720 (time used cannot exceed 720 minutes)
5R+5S<=1500 (carbonated water used cannot exceed 1500 gallons)
2. The same model has been bulit in excel and solved using solver:
Thus, 300 cases of root beer and 0 cases of ornage soda will be made to give a maximum profit of 1,800.
The optimum solution is intutive as the root beer is giving more profit than orange soda. The carbonated water consumed is the same by both the soft drinks and there is an extra minute required per case of making orange soda. Thus intuitively (without using solver or graphical method), one can say that making root beer makes more common sense.
Number of cases of root beer Number of cases of orange soda Time used per case of root beer Time used per case of root beer 300 0 2 3 Profit per case of root beer Profit per case of orange soda Total time for root beer Total time orange soda Total time used 6 4 600 0 600 Total profit for root beer Total profit for orange soda Total profit Carbonated water used per case of root beer Carbonated water used per case of orange soda 1800 0 1800 5 5 Total carbonated water used for root beer Total carbonated water used for orange soda Total carbonated water used 1500 0 1500Related Questions
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