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.