The Manager of a Supermarket Estimates the Average Number of Trips

The manager of a supermarket estimates the average number of trips made to the warehouse from each of the 5 outlets and he wants the warehouse to be closer to the outlets which has high number of average trips. The available data on the distance between the warehouse and the outlets are provided in terms of horizontal and vertical distances. That is, X = horizontal coordinate of the warehouse; and Y = vertical coordinate of the warehouse. The data is shown below.

a. Develop a new unconstrained model that minimizes the sum of the demand-weighted distance defined as the product of the demand (measured in number of trips) and the distance to the warehouse.
b. Solve the model you developed in part a.