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:

Process . Output (units/hr.)

Molding ....... 7

Smoothing ........ 12

Painting ....... 10

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.