dolution

The Molokai Nut Company (MNC) makes four different products from macadamia nuts grown in the Hawaiian Island: chocolate-coated whole nuts (Whole), chocolate-coated nut clusters (Cluster), chocolate-coated nut crunch bars (Crunch), and plain roasted nuts (Roasted). The company is barely able to keep up with the increasing demand for these products. However, increasing raw materials prices and foreign competition are forcing MNC to watch its margins to ensure it is operating in the most efficient manner possible. To meet marketing demands for the coming week, MNC needs to produce at least 1000 pounds of the Whole product, between 400 and 500 pounds of the Cluster product, no more than 150 pounds of the Crunch product, and no more than 200 pounds of the Roasted product. Each pound of the Whole, Cluster, Crunch, and Roasted product contains, respectively, 60%, 40%, 20%, and 100% macadamia nuts with the remaining weight made up of chocolate coating. The company has 1100 pounds of nuts and 800 pounds of chocolate available for use in the next week. The various products are made using four different machines that hull the nuts, roast the nuts, coat the nuts in chocolate (if needed), and package the products. The following table summarizes the time required by each product on each machine. Each machine has 60 hours of time available in the coming week.

Minutes Required per Pound

Machine

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Whole

Cluster

Crunch

Roasted

Hulling

1.00

1.00

1.00

1.00

Roasting

2.00

1.50

1.00

1.75

Coating

1.00

0.70

0.20

0.00

Packaging

2.50

1.60

1.25

1.00

The selling price and variable cost associated with each pound of product is summarized in the following table:

Per Pound Revenue and Costs

Whole

Cluster

Crunch

Roasted

Selling Price

$5.00

$4.00

$3.20

$4.50

Variable Cost

$3.15

$2.60

$2.16

$3.10

a. Formulate an LP model for this problem (i.e., List what is the objective variable, what are the decision variables, what should be the objective function, and list the constraints in a mathematics way.)

b. Create a spreadsheet model for this problem, and solve it using Solver.

c. What is the optimal solution?

 
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