4. Production Planning. The profit function for two products is

Profit 3 1 42 3 48 700

2

1 2

2

52 x 1 x 2 x 1 x2 1

where x1 represents units of production of product 1 and x2 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?