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# Linear Programming/Excel Solver/Sensitivity Report

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1) An auto parts manufacturer produces three different parts: Model A, Model B, and Model C. Model A requires 50 pounds of special alloy steel per unit, 130 minutes of machining time per unit, and 60 minutes of assembly time per unit. Model B requires 25 pounds of special alloy steel per unit, 100 minutes of machining time per unit, and 40 minutes of assembly time per unit. Model C requires 45 pounds of special alloy steel per unit, 120 minutes of machining timer per unit, and 60 minutes of assembly time per unit.

The supplier of the special alloy steel can supply at most 1,000 pounds of the steel next period. Machining time available next period equals 3,000 minutes. Assembly time available next period equals 2,600 minutes. According to Marketing, the amount of Model A produced must be greater than or equal to the total combined amount of Model B + Model C production. Profit per unit equals \$12 for Model A, \$15 for Model B and \$18 for Model C.

a) Formulate the linear programming model: Define the decision variables, the objective function, and the constraints. Ensure that you show the extra work required for the Model A constraint.

b) Create the solver model for this problem. Run the model. Select the Sensitivity Report also. How many of each Model should be produced next period? What is the estimated profit for next period?

c) Based on the Sensitivity Report (include), which would you prefer: an extra pound of the special alloy steel, an extra minute of machining time, or an extra minute of assembly time? Why?

2) Aztec Company manufactures four products on two machines. Each machine is available for 40 hours per week. Machine 1 requires two operators; therefore, the labor time required at Machine 1 is twice the machining time required at Machine 1. Machine 2 requires one operator; therefore, the labor time required at Machine 2 equals the machining time required at Machine 2. There is a maximum of 115 labor hours total available for assignment to the machines (labor is flexible). Hint: you will need only one constraint for labor. Product B must account for at least 25% of the total amount of production. You are given the machining time per product for each unit for each product - show work.

Machine 1 - time/unit (hours)
Product A = 0.8
Product B = 0.6
Product C = 1.2
Product D = 2.0

Machine 2 - time/unit (hours)
Product A = 1.0
Product B = 0.9
Product C = 0.8
Product D = 0.7

Profit/unit
Product A = \$40
Product B = \$24
Product C = \$45
Product D = \$38

a) Formulate the linear programming model. Define the decision variables, the objective function, and the constraints. Show the extra work required for the Product B constraints and for determining the labor time per unit.

b) Create the Solver model. Run the model. Select the Sensitivity Report also. How many of each Product should be produced next period? What is the estimated profit for next period?

c) Based on the Sensitivity report (include), which would you prefer: an extra hour at Machine 1, an extra hour at Machine 2 or an extra hour of labor? Why?