Case Problem 3 (30 points) 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 Cost per Shipment (pounds) ($) 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. An accountant at TJ, Inc. 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 5,000Because demand is running high, it is expected that TJ's will receive man},r more orders than can be satised. TJ's is committed to using the available nuts to maximize prot over the fall season; nuts not used will be given to a local charity. Even if it is not protable to do so, TJ's president indicated that the orders already received must be satised. Perform an analysis of TJ's product-mix problem, and prepare a report for Tl's president that summarizes your ndings. 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. The optimal product mix and the total prot contribution 3. Recommendations regarding how the total prot contribution can be increased if additional quantities of nuts can he purchased 4. A recommendation as to whether TJ's should purchase an additional 1,000 pounds of ahnonds for $1000 from a supplier who overbought 5. Recommendations on how prot contribution could be increased (if at all} if Tl's does not satisfy all existing orders