Homework Problem & TJ's Inc. makes three nut mixes for sale to grocery stores 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. The table also lists the percentage of each nut used in the mix Type of Nut Shipment Cost per Percentage of Percentage of Percentage of Amount shipment Regular Mix Deluxe Mix Holiday Mix Almond 6000 $7,500 15% 20% 25% Brazil 7500 $7,125 25% 20 15%% Filbert 7500 56,750 25%% 20% 15% Pecan 5000 $7,200 10% 20% 25% Walnut 7500 $7,875 25% 20% 20%% TJ's accounting department has analyzed the cost of packaging material, sales price per pound, and so forth, and has 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 the specific types of nuts since the cost can vary greatly in the commodity markets. Customer Sales already received are itemized below. Type of Mix Orders Regular Mix 10,000 Deluxe Mix 3,000 Holiday Mix 5,000 Because demand for their nuts is running high TI's believes that they can sell all of the nuts they have available. TJ's is also committed to fulfilling all existing customer orders (even if not profitable) and is seeking to maximize their profits. 1) Find the optimal product mix and the amount of profit that TJ's can expect to earn. 2) What is the cost of the nuts for the regular, deluxe and holiday mixes? 3) TI's has the opportunity to purchase an additional 1000 pound of almonds for $1,000. Should they buy those almonds and why