Plz answer all parts, and you are allowed to use Excel. Provide Excel screenshots, formulas, and explanations.

3. [20pts) Home-Base, a home improvement and building supply chain, is going to build a new warehouse facility to serve its stores in six cities. The coordinates of these cities (in miles) using the graphical origin (0,0) and the annual truckload trips that supply each store are as follows: Store 1 2 3 4 5 6 Coordinate 20 80 45 145 125 150 60 140 135 125 180 25 Truckload trips 150 100 120 60 200 80 (a) Formulate a nonlinear programming model for this problem using the Euclidean distance and real-valued decision variables. (b) Based on the model in (a), determine the set of coordinates for the new warehouse that will minimize the total miles traveled to the store using the computer. (c) Formulate an integer programming model for this problem using Manhattan distance. (d) Based on the model in (c), determine the set of coordinates for the new warehouse that will minimize the total miles traveled to the store using the computer. (e) Compare the total miles traveled to the stores from (b) and (d). (f) Show the optimal coordinates obtained in (b) and (d) on a map, and identify the closest town to the optimal coordinates of (b) and (d), respectively