**PROBABILITY**

Submit a paper copy of your solution in class. You may use graph paper to solve the optimization problem using the graphical method.

Remember to sign the honors pledge as shown below.

*Problem 1 (15 points)*

A manufacturing firm produces two products. Each product must undergo an assembly process and a finishing process. It is then transferred to the warehouse, which has space for only a limited number of items. The firm has 80 hours available for assembly and 120 hours for finishing, and it can store a maximum of 10 units in the warehouse. Each unit of Product 1 has a profit of $50 and requires 4 hours to assemble and 12 hours to finish. Each unit of Product 2 has a profit of $70 and requires 10 hours to assemble and 8 hours to finish. The firm wants to determine the quantity of each product to produce in order to maximize profit.

Solve the linear optimization problem using the graphical method:

Plot the constraints;

Identify the feasible region; and

Plot the objective function lines and find the optimal solution.

What is the optimal solution? What is the optimal value of the objective function?