Problem:
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:
Q1. Write down the decision variables.
Q2. Write down the optimization statement for the objective function.
Q3. Write down the constraints.
Q4. Solve the LP problem in Excel Solver and write down the optimal solution and optimal value of the objective function