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Tucker Inc. must produce 1,000 Tucker automobiles. The company has four production plants. The cost of producing a Tucker at each plant, along with the raw material and labor needed, is shown in the Table below. The autoworkers' labor union requires that at least 400 cars be produced at plant 3; 3,300 hours of labor and 4,000 units of raw material are available for allocation to the four plants. a) Formulate an LP whose solution will enable Tucker Inc. to minimize the cost of producing 1,000 cars from all plants. Hint: assume xi = number of cars produced at plant i, and express the objective function in thousands of dollars. 120 points) b) Solve the LP by using LINDO and show the LINDO output for this LP in addition to the report of Objective Coefficient Ranges and Righthand Side Ranges. [20 points) c) Suppose that the cost of producing at plant 2 is increased by $1,000. Find the new optimal z- value by using LINDO, and explain how LINDO gets this new optimal z-value by using your calculations. [15 points d) Suppose that the cost of producing at plant 1 is decreased by $3,000. Find the new optimal z- value by using LINDO, and explain how LINDO gets this new optimal z-value by using your calculations. [15 points e) Suppose that 4,100 units of raw material are available. Find the new optimal z-value by using LINDO, and explain how LINDO gets this new optimal z-value by using your calculations. [15 points! f) Suppose that exactly 950 cars must be produced. Find the new optimal z-value, by using LINDO, and explain how LINDO gets this new optimal z-value by using your calculations. [15 points) Labor Raw Material TABLE Cost and Requirements for Producing a Tucker Cost Plant (in Thousands of Dollars) 1 15 2 10 3 9 4 7 2 3 4 5 3 4 5 6