# Product Mix TJ's inc

Topics: Optimization, Variable cost, Nut Pages: 2 (545 words) Published: February 24, 2014
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Problem Statement

Present the cost per pound of the nuts included in the Regular, Deluxe, and Holiday mixes. Discuss the optimal product mix and the total profit contribution. Give recommendations regarding how the total profit contribution can be increased if additional quantities of nuts can be purchased. Give a recommendation as to whether TJ’s should purchase an additional 1000 pounds of almonds for \$1000 from a supplier who overbought. Give recommendations on how profit contribution could be increased (if at all) if TJ’s does not satisfy all existing orders.

Quantitative Results

1. The cost per pound of the almonds is \$1.25 The cost per pound of the Brazil Nuts is \$.95. The cost per pound of the filberts is \$.90. The cost per pound of the pecans is \$1.20. Finally the cost per pound of the walnuts is \$1.05. Therefore, the cost per pound of the Regular Mix is \$1.03, of the Deluxe Mix is \$1.07, of the Holiday Mix is \$1.10 2. The optimal product mix is to produce 17500 pounds of the Regular Mix, 10625 pounds of the Deluxe Mix, and 5000 pounds of the Holiday Mix. The total profit contribution after subtracting the total cost per shipment of the various nuts in the mixes is \$24925. 3. The recommendation to the question “if an additional amount of nuts can be purchased to increase the profit contribution” would be to purchase more almonds and walnuts. By looking at the constraint for the dual prices for almonds you will see for every one pound increase in almonds used, the objective function/profit contribution will increase at a rate of \$8.50. And by looking at the dual prices for walnuts you will see for every one pound increase in walnuts used, the objective function/profit contribution will increase at a rate of \$1.50. 4. If an additional 1000 pounds of almonds were offered at a price of \$1000 from a suppler that overbought, we would recommend TJ’s to purchase the almonds. The reason we recommend this is because TJ’s would be purchasing the almonds...