Problem 1 (40 points): Transportation problem Tiara company has two plants in different locations around the country where they produce drilling bits. Their sales partner has three distribution centers where they ship these drilling bits to their various customers. The plants can produce a given number of bits per week and the expected demand for each distribution center is also known. There is a shipping cost from each plant to each warehouse. Which plant should produce and ship how many bits to which distribution centers to meet the demand at each location with minimum cost? The following Table shows the transportation cost from each plant to each distribution center as well as the total demand of each distribution center and the total supply of each plant. Table 1. Transportation costs, per pound, from production plants to warehouses From/To Center 1 Center 2 Center 3 Plants' supply Plant 1 $25 $85 $25 350 Plant 2 $50 $35 $95 300 Centers' demand 100 350 200 a. (15 points) Formulate the objective function and the necessary constraints using the given information. b. (15 points) What is the transportation strategy (number of each product shipped from each plant to each center) that minimizes the total cost? To do that solve the problem using Excel or Gurobi. Show your results clearly and discuss. c. (10 points) Reformulate the problem for the case that each plant loses 30% of their production (due to and unforeseen disruption). Solve the problem using Excel or Gurobi and discuss your results in detail