The Apex Television Company has to decide on the number of 27" and 20" sets to be produced at one of its factories. Market research indicates that at most 40 of the 27" sets and 10 of the 20" sets can be sold per month. The maximum number of work-hours available is 500 per month. A 27" set requires 20 work-hours and a 20" set requires 10 work-hours. Each 27" set sold produces a profit of $120 and each 20" set produces a profit of $80. A wholesaler has agreed to purchase all the television sets produced if the numbers do not exceed the maxima indicated by the market research.

a. Formulate and solve a linear programming model for this problem on a spreadsheet.

b. Formulate this same model algebraically.

c. Solve this model by using the Graphical Linear Programming and Sensitivity Analysis module in your Interactive Management Science Modules to apply the graphical method?