Tucker Inc. needs to produce exactly 1000 Tucker automobiles. The company has four production plants. Due to differing workforces, technological advances, and so on, the plants differ in the cost of producing each car. They also use a different amount of labor and raw material at each. This is summarized in the following table: Plant Cost (in thousands) Labor Material 1 15 2 3 2 10 3 4 3 a 4 5 4 7 5 r. The labor contract signed requires at least 400 cars to be produced at plant 3; there are 3300 hours of labor and 4000 units of material that can be allocated to the four plants. Answer the following questions, making the best possible use of Excel Solver sensitivity analysis report whenever possible. (1) Formulate a LP model to help Tucker minimize the cost of meeting its demand. (10 Points) (2) Use Excel Solver to obtain an optimal solution to Tuckers problem. What are the current production quantities? What is the current cost of production? (9 Points) (3) How much will it cost to produce one more vehicle? How much will we save by producing one less? (2 Points) (4) How would our solution change if it cost only $8,000 to produce at plant 2? For what ranges of costs is our solution (except for the objective value) valid for plant 2? (2 Points) (5) How much are we willing to pay for a labor hour? (2 Points)