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Product Mix for TJ, Inc. TJ's, Inc., makes three nut mixes for sale to grocery chains...

Product Mix for TJ, Inc.

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 purchased the following shipments of nuts at the prices shown:

Type of Nut

Shipment Amount (pounds)

Cost per Shipment

Almond

6000

$7500

Brazil

7500

$7125

Filbert

7500

$6750

Pecan

6000

$7200

Walnut

7500

$7875


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 already received are summarized here:

Type of Mix

Orders (pounds)

Regular

10,000

Deluxe

3,000

Holiday

5,000

Because demand is running high, TJ's expects to receive many more orders than can be satisfied, but TJ's president indicated that the orders already received must be satisfied.

1. What is the cost per pound of the Regular, Deluxe, and Holiday mixes?

2. Formulate this case problem as a linear program. What is the optimal product mix for TJ? What is the expected total profit contribution? Include a copy of the sensitivity report.

3. Should TJ management consider buying additional almonds, if available? If so, how many pounds should they buy, and what is the maximum price per pound they should pay?

4. Explain the negative shadow price for the required amount of Holiday mix.


5. Assuming TJ could not purchase additional nuts, what else could management do to increase profits? How much more profit could they make?

Solutions

Expert Solution

keosha answered 1 year ago
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