The DullEye Television Company has to decide on the number of 27- and 20-inch television sets to be produced. Market research found that at most 40 of the 27-inch sets and 10 of the 20-inch sets can be sold per month. The maximum number of work hours is 500 per month. A 27-inch set requires 20 work hours and a 20-inch set requires 10 work hours. Each 27-inch set sold produces a profit of $120 and each 20-inch 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, with the additional restriction that they will buy at most twice as many 20-inch sets as 27-inch sets. Required:
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 Pro- gramming and Sensitivity Analysis module in your Interactive Management Science Modules to apply the graphical method.