JR’s Inc., makes three nuts 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 preparing for the fall season, JR’s has just 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 7575
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 nuts, and the Holiday Mix consist of 25% almonds, 15% Brazil nuts, 15% filberts, 25% pecans, and 20% walnuts.
JR’s accountant analyzed the cost of packaging materials, sales price per pound, and so forth, and determined that the profit contribution per pound is $2 for the Regular Mix, $2.40 for the Deluxe Mix, and $2.70 for the Holiday Mix. These figures do not include the cost of special types of nuts in the different mixes because the 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, it is expected that JR’s will receive many more orders that can be satisfied.
JR’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, JR’s president indicated that the orders already received must be satisfied.
Perform and analysis of JR’s product-mix problem, and prepare a report for JR’s president that summarized your findings. 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. Formulate a linear program that can be used to determine the optimal product mix for JR’s Inc. Specifically, do the following: Identify the decision variables (make sure that you specify the units for these variables). Specify the objective function and the relevant constraints. ………………………………………………………………….
3. The production manager uses a DSS to obtain the optimal production mix. The maximum attainable profit is required. Develop a simple DSS prototype to solve this production planning problem.
a. How many pounds of Regular, Deluxe, and Holiday mixes are produced under this optimal product mix?
b. What is the maximum attainable profit?
c. What is the profit contribution for each mix (Regular, Deluxe, and Holiday)? ………………………………………………………………………..
4. Write a short memo to the vice-president of production outlining the following: ………………………………………………………………………………..
a) Recommendations regarding how the total profit contribution can be increased if additional quantities of nuts can be purchased
b) Recommendation as to whether JR’s should purchase an additional 1,000 pounds of almonds for $1,000 from a supplier who overbought
c) Recommendations on how profit contribution could be increased (if at all) if JR’s does not satisfy all existing orders.