TJ’s Inc., makes three nut mixes for sale to grocery chains located in the Southeast. The three mixes, referred to as Regular Mix, Deluxe Mix, and 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 at the prices shown.
Type of Nut Shipment Amount (Pounds) Total Cost
Almond 6,000 $7,500
Brazil 7,500 $7.125
Filbert 7,500 $6,750
Pecan 6,000 $7,200
Walnut 7,500 $7,875

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 has 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. These figures do not include the cost for the specific types of nuts in the different mixes because that cost can vary greatly in the commodity markets. 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.
TJ’s is committed to using the available nuts to maximize profit over the fall season; nuts not used will be given to the free store. Even if it is not profitable to do so, TJ’s president has 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 finding. Be sure to include information and analysis on the following:
1. The cost per pound of the nuts included in the Regular, Deluxe, and Holiday mixes.
2. The optimal product mix and the total profit contribution.
3. Recommendations regarding how the total profit contribution can be increased if additional quantities of nuts can be purchased.
4. A recommendation as to whether TJ’s should purchase an additional 1,000 pounds of almonds for $1,000 from a supplier who overbought.
5. Recommendations on how profit contribution could be increased (if at all) if TJ’s does not satisfy all existing orders.