The Apex Television Company has to decide on the number of 65” and 55” sets to be produced at one of its factories. Market research indicates that at most 280 of the 65” sets and 70 of the 55” sets can be sold per month. The maximum number of work hours available is 3,500 per month. A 65” set requires 20 hours and a 55” set requires 10 work hours. Each 65” set sold produces a profit of $270 and each 55” setting produces a profit of $180. A wholesaler has agreed to purchase all the television sets produced if the numbers do not exceed the maxima indicated by the market research.

1. Formulate and solve a linear programming model for this problem on a spreadsheet.
2. Formulate this same model algebraically.
3. Use the graphical method to solve this model. ( Mention the corner/extreme points)