The production planner for a private label soft drink maker is planning the prod

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

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2.

As per the excel solver, the solution comes to 12.5 cases of root beer only to be produced to optimise profits. Technically, this solution cannot be correct although intutive in nature, since then there is a complete wastage of time. Factors clearly affecting the production other than the time frame and material used should also be mentioned for the problem to give a more correct picture.

Consider the following 2 variable linear programming problem: Maximize: 6 R + 4 S Subject to: Constraint 1      R/30 +        S/20 <= 12 Constraint 2 120R + 120S <= 1500 R S Number of 0 0 obj. fun. Profit 6 4 =SUMPRODUCT(B$8:C$8,B9:C9) LHS RHS Constraint 1 2/60 3/60 =SUMPRODUCT(B$8:C$8,B11:C11) 12 Constraint 2 120 120 =SUMPRODUCT(B$8:C$8,B12:C12) 1500 Wherein, R is the no. of cases of Root Beer Produced S is the no. of cases of Orange Soda Produced Since one case of root beer requires 2 minutes of time, in hours it is equivalent to 2/60 = 1/30 Since one case of orange soda requires 3 minutes of time, in hours it is equivalent to 3/60 = 1/20 1 case = 24 bottles Hence for 1 case of root beer = 5 X 24 = 120 gallons of water is required For 1 case of orange soda = 5 X 24 = 120 gallons of water is required

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