Reference no: EM13590685

A firm makes six types of juice-blends. They are A) Orange-Pineapple, B) Orange-Pineapple-Mango, C) Orange-Kiwi-Strawberry, D) Orange-Pineapple-Strawberry-Mango, and H) Pure Orange. The following table lists all the relevant data.

The ingredient availability is: Orange-Juice = 28,000 gallons, Pineapple Juice = 140,000 gallons, Strawberry Juice = 130,000 gallons, Kiwi Juice = 100,000 gallons and Mango Juice = 80,000 gallons.

The sale price of the blends A through E are listed in the table above. Costs of the juices used the production of the blends are: Orange $1.20/gal, Kiwi $2.20/gal, Pineapple $1.30/gal, Strawberry = 1.70/gal and Mango is $2.80/gal. Note that you do not have any inventory of the juices and everything musts be bought.

Other restrictions:

1)Blend A has to be at least 10% of the total production

2)Blend B and C together cannot be more than 20% of the other four blends.

3)Blend F must account for at least 50% of the total of all blends.

4)Consumption of Kiwi Juice cannot exceed 30% of OJ consumption.

5)Consumption of Pineapple Juice cannot exceed 40% of OJ consumption.

Set this up as an Linear Program with the decision variable as quantities of the blends to be produced with the objective of maximizing profit. Use the names of variables as A, B, C, D, E and F.

Q1)Write down the complete LP in algebraic form

Q2)Solve it and provide the answer. Write the optimal solution in plain English.

Q3)Provide a picture copy of the xl screen to fit in one page showing the optimal solution.