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A widget factory employs apprentice workers and master workers across two work shifts every day. An apprentice worker costs $140 per day to hire and can produce 3 units during 1st shift or 2 units during 2nd shift. A master worker costs $280 per day to hire and can produce 7 units during 1st shift or 6 units during 2nd shift. The company has a total hiring budget of $3700 per day. The union contract has two additional stipulations: .There must be at least one master worker for every 2 apprentice workers in each shift. The number of master workers hired on 2nd shift must be 8 or fewer. The company wants to hire workers for each shift in order to maximize the total number of units produced. Set up this problem as a linear programming problem which could be solved using the simplex method. Be sure to include the following information: a. Define each decision variable. b. Write each constraint as an inequality using the decision variables. c. Write the objective function. Is it maximized or minimized? d. Set up the problem as a system of inequalities. e. Set up the initial simplex tableau, but do not solve.