# Using LP Model for determining maximum profit

Wineco produces wine cooler as a blend of wine, grape juice and apple juice ingredients, which it sells for $4 per gallon. The costs of ingredients are given in the following table:

Cooler

Ingredient Price per Gallon($)

wines 1.20

grape juice 1.40

Apple juice 0.60

Wineco owns a blending plant with a production capacity of 200 gallons per day. Because the plant is fully automated, all other production costs are negligible by comparison to the cost of ingredients, and can be ignored. Government regulations mandate that wine cooler products must satisfy the following guidelines:

1.At least 10% of the blend produced must be grape juice.

2.The ratio of apple juice to grape juice in the blend produced must be 2.5:1

3.The blend produced must contain between 20% and 25% wine.

Wineco wishes to use LP in order to determine the quantities of ingredients to buy for a day's production of wine cooler, so as to maximize net profit.

Answer the following questions:

3.1)Write down the decision variables.

3.2)Write down the optimization statement for the objective function.

3.3)Write down the constraints.

3.4)Solve the LP problem in Excel Solver and write down the optimal solution and optimal value of the objective function (attach the spreadsheet screenshot).

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#### Solution Preview

Please see the attached file(s) for complete details of Excel snapshot and working with Solver.

Solution:

3.1)Write down the decision variables.

Let x1 be the amount of wines in cooler needed in one day's production

X2 be amount of grape juice in cooler in one day's production

X3 be amount of apple juice in cooler in one day's production

3.2)Write down the optimization statement for the objective function.

Profit = Revenue - ...

#### Solution Summary

Solution describes the steps in formulating linear programming model for wine cooler which contains a combination of wines, apple and grape juice. Connstraints are written in algabraic form from given various mixing limits. Then it explains the steps in solving LP model with the help of Excel Solver.