Introduction to Management Science 12th Edition by Bernard Taylor

Exercise 11

Assume that the objective function in Problem has been changed from Z = 30 x 1 + 70 x 2 to Z = 90 x 1 + 70 x 2. Determine the slope of each objective function and discuss what effect these slopes have on the optimal solution.
Problem
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