Introduction to Management Science 12th Edition by Bernard Taylor

Exercise 43

A manufacturer of bathroom fixtures produces fiberglass bathtubs in an assembly operation that consists of three processes-molding, smoothing, and painting. The number of units that can undergo each process in an hour is as follows:
( Note: The three processes are continuous and sequential; thus, no more units can be smoothed or painted than have been molded.) The labor costs per hour are $8 for molding, $5 for smoothing, and $6.50 for painting. The company's labor budget is $3,000 per week. A total of 120 hours of labor is available for all three processes per week. Each completed bathtub requires 90 pounds of fiberglass, and the company has a total of 10,000 pounds of fiberglass available each week. Each bathtub earns a profit of $175. The manager of the company wants to know how many hours per week to run each process to maximize profit.
a. Formulate a linear programming model for this problem.
b. Solve the model by using the computer.