Location Problem

By Muhammad Al-Salamah

Akhawain Meat Factory is trying to determine where it should locate a single warehouse. The positions in the x-y plane in km of four supermarkets and the number of shipments made yearly to each supermarket are given as

Akhawain wants to locate the warehouse to minimize the total distance trucks must travel yearly from the warehouse to the the four supermarkets.

Define the variables:

x = x-coordinate of warehouse

y = y-coordinate of warehouse

d_i = distance from warehouse to supermarket i

The optimization problem is