A product is produced at three plants and shipped to three warehouses. Plant capacity, warehouse demands and transportation costs per unit are shown in the table. Plant 1 2 3 Warehouse Demands A 20 10 12 200 Warehouse B 16 10 18 400 C 24 8 10 600 Plant Capacity 300 500 400 a) Formulate the Linear Programming model for this problem. b) Find an initial feasible solution and calculate the cost for this solution. c) If improvement can be made, make one step improvement to the solution in part a, and calculate the cost for the improved solution. let's assume that 3 sites with the following coordinates are being considered. Which one do you recommend? Show your work to support your decision. A (X=52, Y=14), B(X= 16, Y= 33), C (X= 20, Y= 30) 2- The AID Parcel Service wants to build a new distribution center in Charlotte. The center needs to be in the vicinity of Inerstate-77 and Intersatate-85 interchanges, and the Charlotte International Airport. The coordinates of these three sites and the number of weekly packages that flow to each are as follows: 1-77 X=10 Y=28 W=16,000 1-85 X=35 Y=18 W=22,000 Airport X=40 Y=18 W=10,000 Determine the best site location using the center-of-gravity technique. (Show your work)