Management Science – Case Study

Case Study I: Product Mix

TJ’s, Inc., makes three nut mixes for sale to grocery chains located in the Southeast. The three mixes,

referred to as the Regular Mix, the Deluxe Mix, and the Holiday Mix, are made by mixing different

percentages of five types of nuts.

In preparation for the fall season, TJ’s has just purchased the following shipments of nuts:

Type of Nut Shipment Amount (lbs)

Almond 6000

Brazil 7500

Filbert 7500

Pecan 6000

Walnut 7500


The Regular Mix consists of 15% almonds, 25% Brazil nuts, 25% filberts, 10% pecans, and 25% walnuts.

The Deluxe Mix consists of 20% of each type of nut, and the Holiday Mix consists of 25% almonds, 15%

Brazil nuts, 15% filberts, 25% pecans, and 20% walnuts.

TJ’s accountant analyzed the cost of packaging materials, sales price per pound, and so forth, and

determined that the profit contribution per pound is $1.65 for the Regular Mix, $2.00 for the Deluxe

Mix, and $2.25 for the Holiday Mix.

Customer orders have already been received and are summarized here:

 Regular Mix 10,000 lbs

 Deluxe Mix 3,000 lbs

 Holiday Mix 5,000 lbs

Because demand is running high, it is expected that TJ’s will receive many more orders than can be

satisfied. TJ’s is committed to using the available nuts to maximize profit over the fall season; nuts not

used will be given to a local charity. Even if it is not profitable to do so, TJ’s president indicated that the

orders already received must be satisfied.

Perform an analysis of TJ’s product-mix problem, and prepare a report for TJ’s president that

summarizes your findings.

1. Formulate this LP problem using steps 1-4. This will be considered a homework assignment due

prior to the written portion of the assignment.

2. In your writing assignment, you are taking the position as the production analyst for TJ’s, Inc.

Write the report in a memo style format summarizing all of the essential information, results,

and recommendations. The memo should be about two pages long, single-spaced.

3. Be sure to include information on what the optimal product mix is and the total profit


4. Given the optimal solution order information, how many pounds of nuts will TJ’s be donating to charity?

5. If additional nuts can be purchased, which nuts should TJ’s buy and why? Up to how many

pounds can be purchased before affecting the optimal solution?

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