5. A food firm is researching the profitability of introducing six new "healthy choice" food products (call them x, y, z, a, b, c). The firm currently has idle resource capacity on labor, machinery, and land of 100 hours, 300 hours, and 30,000 square feet, respec- tively. Hence, producing any or all of the new products will help solve the costs of excess capacity. The selling prices, total costs, and resource requirements for the pro- duction technology are summarized below. New Product Resource (Unit) X Z b Labor (hours) 0.50 0.10 1.00 0.45 0.20 0.15 Machinery (hours) 1.00 0.45 3.50 1.00 1.10 2.00 Land (sq ft) 100 200 50 25 10 75 Unit Costs ($) 10 3 33 22 12 9 Unit Price ($) 12 36 23 15 11 Food products y and z are complements in the sense that for every unit of y produced and sold, 2 units of z must be produced and sold. Also, the firm requires that the amount of product c produced and sold be at least 50% of the total units of products a and b that are produced and sold. Set up an LP model that will result in a solution that maximizes total profit from the sale of any combination of these food products, subject to all constraints that were specified. 6. Now suppose that the firm in Exercise 5 can hire additional labor at $8 per hour. Reformulate Exercise 5 to allow for the firm to hire up to an additional 500 hours of labor. Note that now hired labor should be modeled as an activity in Exercise 5