# Plot the objective function lines and find the optimal solution. What is the optimal solution? What is the optimal value of the objective function?

PROBABILITY

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

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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?

Plot the objective function lines and find the optimal solution. What is the optimal solution? What is the optimal value of the objective function?