Final Exam -LP (25 pts) - Word References Mailings Review View Tell me what you

Question

Final Exam -LP (25 pts) - Word References Mailings Review View Tell me what you want to do Product Mix L.M. Nuts, Inc., makes three nut mixes for sale to grocery chains located in the Pacific Northwest. 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, October -December, L.M. Nuts, Inc, purchased the following shipments of nuts at the prices shown: Type of Nut Shipment Amount (Ibs) Cost per Shipment Almond Brazil Filbert Pecan Walnut 7500 7500 6000 7500 7,500 7,125 750 $7,200 Note that the cost of the five shipments of nuts is a sunk (not a relevant) cost and should not affect the decision. However, this information may be mseful to management in future pricing and purchasing decisions. Each L.M. Nuts, Inc., mix (i.e., Regular, Deluxe and Holiday) are comprised of the five types of nuts shown above, with the following composition or combination: Ingredient Contribution (%) Type of Mix Almond Brazill Filbert Pecan Walnut Deluxe Holiday 15 20 25 20 15 25 20 15 25 20 20 25 The Accounting Department analyzed the product cost (ie., production, packaging materials, orders, inventory, etc.) and sales price per pound, 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 of specific types of nuts in the different mixes because that cost can vary greatly in the commodity markets. Because demand is running high, I.M. Nuts, Inc, expects to receive many more orders than can be satisfied. Customer orders already received (in lbs): Regular-10,000; Deluxe-3,000, Holiday-5,000. I.M. Nuts, Inc., is committed to using the available nuts to maximize profit over the Fall Season, October - December. Nuts not used will be given to local food shelters. Even if it is not profitable to do so, the President of I.M. Nuts, inc., the head nut, indicated that the orders already received must be satisfied Perform an analysis of the 1.M. Nuts, Inc., product mix problem

Explanation / Answer

Decison Variables: Let R, D and H represent the qty (in pounds) of Regular, Deluxe and Holiday mixture to be produced.

Objective function: Maximize Z = 1.65R + 2D + 2.25H

s.t. Constraints:

0.15R+0.2D+0.25H 6000

0.25R+0.2D+0.15H 7500

0.10R+0.2D+0.25H 6000

0.25R+0.2D+0.2H 7500

R,D,H >=0

Optimal product mix: Regular = 17500 pounds , Deluxe = 10625, Holiday = 5000

Total profit contribution = 61,375

2) No, he should not purchase Brazil nut, because existing stic is not fully utilized. So purchasing additional Brazil nuts is not required.

3) Yes, additional units of Almons should be purchased at this price. Because Almonds is binding constraint. Shadow price is 8.5, which means unit increase in Almonds qty will result in $ 8.5 increase in p

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