An Introduction to Management Science 13th Edition by David Anderson,Dennis Sweeney ,Thomas Williams ,Jeffrey Camm, Kipp Martin

Exercise 18

The profit function for two products is
Where x 1 represents units of production of product 1 and x 2 represent units of production of product 2. Producing one unit of product 1 requires 4 labor-hours and producing one unit product 2 requires 6 labor hours. Currently, 24 labor-hours are available. The cost of labor-hours is already factored into the profit function. However, it is possible to schedule the overtime at a premium of $5 per hour.
a. Formulate an optimization problem that the can be used to find the optimal production quantity of products 1 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?