Worley Fluid Supplies produces three types of fluidhandling equipment: control valves, metering pumps, and hydraulic cylinders. All three products require assembly and testing before they can be shipped to customers.

Control Valve Metering Pump Hydraulic Cylinder Assembly time (min) 45 20 30 Testing time (min) 20 15 25 Profit/unit $372 $174 $288 Maximum sales 20 50 45 Minimum sales 5 12 22 A total of 3,150 minutes of assembly time and 2,100 minutes of testing time are available next week.

a. Develop a linear optimization model to determine how many pieces of equipment the company should make next week to maximize profit contribution.

b. Implement your model on a spreadsheet and find an optimal solution.

c. Explain the sensitivity information for the objective coefficients. What happens if the profit on hydraulic cylinders is decreased by $10?

d. Due to scheduled maintenance, the assembly time is expected to be only 3,000 minutes. How will this affect the solution?

e. A worker in the testing department has to take a personal leave because of a death in the family and will miss 3 days (24 hours). How will this affect the optimal solution?

f. Use the auxiliary variable technique to handle the bound constraints and generate all shadow prices.