San Diego State University Operations And Supply Chain Management Assignment Help - Linear

Question - Georgia Cabinets manufactures kitchen cabinets that are sold to local dealers throughout the
Southeast. Because of a large backlog of orders for oak and cherry cabinets, the company decided to
contract with three smaller cabinetmakers to do the final finishing operation. For the three
cabinetmakers, the number of hours required to complete all the oak cabinets, the number of hours
required to complete all the cherry cabinets, the number of hours available for the final finishing
operation, and the cost per hour to perform the work are shown here:


For example, Cabinetmaker 1 estimates they will take 50 hours to complete all the oak cabinets and
60 hours to complete all the cherry cabinets. However, Cabinetmaker 1 only has 40 hours ...Read More available
for the final finishing operation. Thus, Cabinetmaker 1 can only complete 40/50 = 0.80, or 80%, of the
oak cabinets if they worked only on oak cabinets. Similarly, Cabinetmaker 1 can only complete 40 =
60 = 0.67, or 67%, of the cherry cabinets if they worked only on cherry cabinets.
a. Formulate a linear programming model that can be used to determine the percentage of the oak
cabinets and the percentage of the cherry cabinets that should be given to each of the three
cabinetmakers in order to minimize the total cost of completing both projects.
b. Solve the model formulated in part (a). W hat percentage of the oak cabinets and what percentage
of the cherry cabinets should be assigned to each cabinetmaker? What is the total cost of completing
both projects?
c. If Cabinetmaker 1 has additional hours available, would the optimal solution change? Explain.
d. If Cabinetmaker 2 has additional hours available, would the optimal solution change? Explain.
e. Suppose Cabinetmaker 2 reduced their cost to $38 per hour. W hat effect would this change have
on the optimal solution?Explain. ...Read Less

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