PLEASE ANSWER AS SOON AS POSSIBLE!!!

Please use the Lindo software to solve the problems where needed.

Also please explain the background on how The Lindo software computes the value for each question.

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 autonomous' 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 x = mumber of cars produced at plant i, and express the objective function in thousands of dollars. [20 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. 120 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. 126 points 1) 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 2-alue by using your calculations. 115 points) TABLE Cast and Requirements for Producing a Tucker Cust Plant Cin Thousands of Dollars 15 10 Labor Raw Material 3 2 3 1 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 autonomous' 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 x = mumber of cars produced at plant i, and express the objective function in thousands of dollars. [20 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. 120 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. 126 points 1) 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 2-alue by using your calculations. 115 points) TABLE Cast and Requirements for Producing a Tucker Cust Plant Cin Thousands of Dollars 15 10 Labor Raw Material 3 2 3 1