Instructions: do all your computational work and show your final answers clearly. if you do not show your computational work, you will not receive credit. problem i: 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 just purchased the following shipments of nuts as shown: type of nut shipment amount (pounds) almond 6000 brazil 7500 filbert 7500 pecan 6000 walnut 7500 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. customer orders already received are summarized here: type of mix orders (pounds) regular 10,000 deluxe 3,000 holiday 5,000 school of business norfolk state university – an equal opportunity employer because demand is running high, it is expected that tj, inc. will receive many more orders than can be satisfied. tj, inc. 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, inc.’s president indicated that the orders already received must be satisfied. 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 optimal product mix and the total profit contribution; 2. a recommendation as to whether tj, inc. should purchase additional quantities of brazil nuts; 3. a recommendation as to whether tj, inc. should purchase an additional 1000 pounds of almonds for $1000 from a supplier who overbought.