Case Problem 1. Product Mix TJ, Inc.'s 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, Inc.'s has just purchased the following shipments of nuts at the prices shown: Type of Nut Almond Shipment Amount (pounds) 6000 7500 Cost per Shipment ($) 7500 Brazil 7125 Filbert 7500 6750 7200 Pecan 6000 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. Managerial Report Perform an analysis of the TJ, Inc.'s product-mix problem, and prepare a report for the president of TJ, Inc. that summarizes 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. Now that you have calculated the cost per pound of the mixes and you have the profit contribution of the mixes, what is the suggested retail price per pound of Regular Mix, Deluxe Mix, and Holiday Mix? 3. Develop a linear programing mathematical model showing the Objective Function to maximize profit, and all the constraints based on the information provided in the case. 4. Create an Excel model for this problem and solve it using Solver. What is the optimal profit and the value of the variables