A television set manufacturer makes two models of TV sets, LED and HD, and in two sizes, 32" and 55". The firm has to decide on the mix of the combinations of the two models and the two sizes. A market research indicates that at most 2000 of 32" (both models combined) and at most 4000 of 55" TV sets (both models combined) can be sold per month. In addition, past sales records indicate that the combined sales for both sizes of HD TV sets is at least twice the combined sales of the two sizes of LED TV sets. The maximum number of labor-hours available is 30,000 per month. A 32" LED TV set requires 10 labor-hours, a 55" LED TV requires 14 labor-hours, while a 32" HD TV set requires 12 labor-hours and a 55" HD TV set requires 16 labor-hours. The unit profit of a 32" LED, 32" HD, 55" LED and 55" HD TV set is $80, $100, $130 and $140, respectively. It is desired to find the number of TV sets to produce per month for these two sizes and models in order to maximize monthly profit. Formulate a linear programming model for this problem (define variables and setup the objective function and the constraints; also describe in a few words what your objective function and each of your constraints represents). Do not solve. The company has a fixed workforce that does not plan to change. Therefore the only way to increase labor-hours is by overtime. Suppose that at most 6000 extra labor-hours can be obtained by allowing overtime at the average of $30 per hour. Show how you modify the formulation above to find if and how many hours of overtime should be used per month. Do not solve.