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 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. 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, but TJ's president indicated that the orders already received must be satisfied. Managerial Report Perform an analysis of TJ's product mix problem, and prepare a report for TJ's president that summarizes your findings. Be sure to include information and analysis on the following: 1. What is the cost per pound of the Regular, Deluxe, and Holiday mixes 2 2. Formulate this case problem as a linear program. What is the optimal product mix for TJ? What is the expected total profit contribution include a copy of the sensitivity report 3. Should TJ management consider buying additional almonds, if available? If so, how many pounds should they buy, and what is the maximum price per pound they should pay? 4. Explain the negative shadow price for the required amount of Holiday mix, 5. Assuming TJ could not purchase additional nuts, what else could management do to increase profits? How much more profit could they make