Essentials of Business Analytics 1st Edition by Jeffrey Camm,James Cochran,Michael Fry,Jeffrey Ohlmann ,David Anderson

Exercise 5

The profit function for two products is:

where x 1 represents units of production of product 1, and x 2 represents units of production of product 2.
Producing one unit of product 1 requires 4 labor-hours, and producing one unit of product 2 requires 6 labor-hours. Currently, 24 labor-hours are available. The cost of labor-hours is already factored into the profit function, but it is possible to schedule overtime at a premium of $5 per hour.
a. Formulate an optimization problem that can be used to find the optimal production quantity of products 1 and 2 and the optimal number of overtime hours to schedule.
b. Solve the optimization model you formulated in part a. How much should be produced and how many overtime hours should be scheduled