Niketa Sports Company manufacturers treadmills in factories located in Pittsburgh and Kansas City. These are shipped to regional distribution centers in Chicago, Phoenix, and Philadelphia. Ultimately they are delivered to supply houses in New York and Los Angeles. The available supplies at the factories, demands at the final destinations, and shipping costs are illustrated in the table below.
To: Chicago To: Phoenix To: Philadelphia To: New York To: Los Angles Supply
From: Pittsburgh $4 $8 $2 -- -- 1500
From: Kansas City $3 $6 $5 -- -- 1000
From: Chicago -- -- -- $5 $7 --
From: Phoenix -- -- -- $8 $3 --
From: Philadelphia -- -- -- $2 $9 --
Demand -- -- -- 1200 800 --
Part 1. Formulate this problem as a linear program.
Let (1) = Pittsburgh, (2) = Kansas City, (3) = Chicago, (4) = Phoenix, (5) = Philadelphia, (6) = New York, and (7) = Los Angeles
Let xij = the number of units shipped from location i to location j.
Part 2.
Determine how many units should be shipped for all possible origin and destination points (final or intermediate) in the distribution network in order to minimize shipping costs.