Directions:
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?
