Case Problem 1 PRODUCT MIX 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 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 7875 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. 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. 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 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.
ANSWER THE FOLLOWING
Sensitivity reports for linear programming are a a vital tool for proper interpretation and application. This week, we look into how this is done in more detail and how to apply to real-world situations.
Please respond to all of the following prompts:
Read through Case Problem 1, page 355.
a) In what type of circumstances would it be better to incorporate sensitivity analysis?
b) What purpose does Shadow Price serve in actual business cases? Find an example via internet searches.