Problem 2 (20 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 112 hours for finishing, and it can store a maximum of 10 units in the warehouse. Each unit of product 1 has a profit of $30 and requires 4 hours to assemble and 14 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. a. Formulate a linear programming model for this problem. b. Solve this model by using graphical analysis. c. Assume that the objective function has been changed from 2 = 30,1 + 70ry to Z = 90+ 70.rg. Determine the slope of each objective function and discuss what effect these slopes have on the optimal solution