The profit function for two products is:
    Profit = −3x12 + 42x 1 − 3x22 + 48x 2 + 700,
where x 1 represents units of production ofproduct 1, and x 2 represents units ofproduction of product 2. Producing one unit of product 1 requires 5labor-hours, and producing one unit of product 2 requires 6labor-hours. Currently, 24 labor-hours are available. The cost oflabor-hours is already factored into the profit function, but it ispossible to schedule overtime at a premium of $5 per hour.
Formulate an optimization problem that can be used to find theoptimal production quantity of products 1 and 2 and the optimalnumber of overtime hours to schedule.
Solve the optimization model you formulated. How much should beproduced and how many overtime hours should be scheduled? Ifneeded, round your answers to two decimal digits.
| Amount | |
| Product 1 | | units |
| Product 2 | | units |
| | |
| Overtime Used | | hours |
