M3_A1. Tuskaseigee Pottery Company is a small business that produces clay bowls and mugs. The two resources used by the company are special North Carolina clay and labor. Given that they only have resources that want to know how many bowls and mugs that they should produce to maximize profit. The two products have the following resource requirements for each type of item produced. There are 40 hours of labor and 120 pounds of clay available each day for production. Solve this two decision variable problem using the LP Graphing utility. Resource Requirements Product Labor (hrs./unit) Clay (lbs./unit) Profit ($/unit) Bowl 1 4 40 Mug 2 3 50 a) What is the profit (value of the objective function) for the optimal solution? b) How many bowls should be produced each day? c) How many mugs should be produced each day? d) Is the production of 10 mugs and 10 bowls feasible (not asking if it is optimal). Does it fall in the feasible region? e) Is the production of 15 mugs and 15 bowls feasible (not asking if it is optimal). Does it fall in the feasible region? 2 M3_A2. An electronics corporation manufactures five highly technical products (V1, W2, X3, Y4, and Z5) that it supplies to communications firms. Each of the products must pass through Department A, Department B, and Department C before being shipped. The time available in each department each month, minimum production levels for each product, and unit profit is summarized in the following table. Formulate and solve the problem in Excel to determine the number of each product to manufacture that meets the requirements and maximizes profits.