Please provide a full solution of the Case Study questions.

OPERATIONS MANAGEMENT CASE STUDY A transportation company has signed supply contracts with ten production plants. These plants are located in the (map) coordinates given below: Talue a. werruannies on wis prants To reduce its operatin ; costs, the company is considering opening a new supply center. This center would be used to serve the raw materials required by these ten plants. 1. Assuming that the gc al of the company is to minimize the distance from the supply center to the plants, where (at vhich coordinates) would you locate it? You must describe the mathematical model o be used, implement it in Excel and solve it. Include a diagram that shows the location of all plants and the proposed location of the supply center. Hint: The (Euclidean) distance between two points a(acaz) and b(bcbc) on a plane is defined as d(a,b)=(a1b1)2+(2b2)2. 2. In practice, not all plants require the same amount of raw materials. The number of trips (per month) necessary to supply each plant is shown in Table 2. What would be the optimal location of the supply center taking into account this information? What is the impact on the solution of the different amounts demanded by each plant? You must describe the mathematical model to be used, implement it in Excel and solve it. Include a diagram that shows the location of all plants and the proposed location of the supply center. Tabie 2 . Nunter on wips. 3. For the situation described in question 1 (minimize the total distance assuming a single trip to each plant), what would be the consequences of losing Plant 5 as a customer? Would the optimal location of the supply center be affected? How? 4. Going back to the situation described in question 2, assume that you could open two supply centers. Center 1 will serve plants 1,2,5,6,10 and Center 2 will serve the rest. Write down the model for this new problem, implement it in Excel and include a diagram with the proposed location of the two centers