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The Primo Insurance Company is introducing two new product lines: special risk insurance and mortgages. The expected profit is $5 per unit on special risk insurance and $2 per unit on mortgages. Management wishes to establish sales quotas for the new product lines to maximize total expected profit. The work requirements are as follows: Department Underwring Administration Claims Work-hours per unit Special Risk Mortgage 3 2 0 1 2 0 Work-hours available 2400 800 1200 a. b. C. d. e. f. Formulate a linear programming model for this problem. Use the graphical methods to solve this model. Is there any unused resource? If so, how much? Are there any redundant constraints? If so, which ones? Which constraints are binding? Explain. What are the values of the slack variables at the optimal solution? 0 2. Weenies and Buns is a food processing plant which manufactures hot dogs and hot dog buns. They grind their own flour for the hot god buns at a maximum rate of 200 pounds per week. Each hot dog bun requires 0.1 pound of flour. They currently have a contract with Pigland, Inc., which specifies that a delivery of 800 pounds of pork product is delivered every Monday. Each hot dog requires 7 pound of pork product. All the other ingredients in the hot dogs and hot dog buns are in plentiful supply. Finally, the labor force at Weenies and Buns consists of 5 employees working full time (40 hours per week each). Each hot dog requires 3 minutes of labor, and each hot dog bun requires 2 minutes of labor. Each hot dog yields a profit of $0.88, and each bun yields a profit of $0.33. Weenies and Buns would like to know how many hot dogs and how many hot dog buns they should produce each week so as to achieve the highest possible profit. a. Formulate a linear programming model for this problem. b. Use the solver to solve this model. C. What are the dual values? d. How would the decision change if the expected profit per unit on a hot dog become $2? e. Would the decisions and the objective value change if an employee was fired? Explain. f. If you could choose to change the right-hand side of one constraint by 1 unit. Which one would you change and why