Problem 1 The R& D division of the Progressive company has been developing 4 possible product lines. Management must make a decision on which of the 4 products will be produced and at what levels to maximize the profit. The start-up cost and marginal revenue for each product is given in the following table: Product 1 2 3 4 Start-up cost $50,000 $40,000 $70,000 $60,000 Marginal revenue $ 70 $ 60 $ 90 $ 80 Let continuous variables X1, X2, X3, 24 be the production levels of product 1,2,3 and 4, respec- tively, and let binary variables y1, 42, 43, 44 control whether or not each product is produced at all. Suppose the manager has imposed the following constraints: No more than two types of the products can be produced. Either product 3 or 4 can be produced only if either product 1 or 2 is produced. Either 5.21 +3.22 + 6.13 + 4.24