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 (pounds)

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 already received are summarized here:

Type of Mix Order (pounds)

Regular 10,000

Deluxe 3,000

Holiday 5,000

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.

Summarize the model in algebraic form by defining the decision variables, the objective function

and all the constraints. Do not solve it.