The Rescarch and Development Division of the Progressive Company has been developing four possible new product lines. Management must now make a decision as to which of thesic four. products actually will be produced and at what levels. Therefore, an operations research study has been requested to find the most profitable product mix. A substantial cost is associated with beginning the production of any product, as given in the first row of the following table. Additionally, the net revenue per unit of each product is shown in second row. Management's objective is to find the product mix that maximizes the total profit (total net revenue minus start-up costs). Furthermore, the company needs to determine which of their available machinery to dedicate to the manufacturing of the new products. The two possible machines are shown below, along with the amount of time each requires to produce one unit of cach potential product. The following constraints also apply: - No more than two products can be produced - You can only produce Product 3 if Product 1 is produced - Only one machine can be used (Hint: you will need to Big-M considerations for this constraint) - The total time available for production should not exceed 6.000 hours Mathematically formulate a linear mixed integer (with binary considerations) programming model for the problem. Youmay not produce frnctional products. You will have three sets of decision variables: - xi:1 if product i is selected for production, 0 otherwise: i=1,2,3,4 - Q: The amount of product i produced; i=1,2,3,4 - 2;1 if machine j is selected, 0 otherwise; j=1,2 Clearly define your decision variables, objective function, and constraints, and combine into a complete mathematical programming model