MNM, Inc. is trying to determine how much of each of three products should be produced over the coming planning period. The only serious constraints involve labor availability in the assembly and packaging departments. Shown below is information concerning the amount of time each product requires in the two departments and the products' profit per unit. Product 1 Product 2 Product 3 Profit/Unit $89 $175 $195 Assembly Minutes per unit 20 35 40 Packaging Minutes per unit 12 28 15 At the present time, there are 360 hours of assembly and 180 hours of packaging available on the regular time. However, the company wants to schedule 48 hours of overtime in the assembly department and 18 hours in the packaging department for a cost of $48 and $18 per hour, respectively. O a. Formulate a linear programming model that can be used to determine optimal production quantities and the amount of overtime in each department Write your problem formulation. b. Solve the LP model and obtain sensitivity analysis. What are the optimal production quantities and the amount of overtime in each department? What is the total profit? Are there any slacks or surpluses? Explain what they mean. c. Refer to the sensitivity analysis and fully explain the meaning of each reduced cost value. d. Refer to the sensitivity analysis and fully explain the meaning of each dual price value.