Mogul Products is a medium-sized manufacture of small appliances in the Midwest. They have three production facilities which can ship to either of two large warehouses. These warehouses, in turn, ship product to four different retailers. (The retailers then transport the items to their retail stores, but that is not an issue for Mogul.)
Plant A has a monthly production capacity of 2500 units. Plant B can produce up to 1500 units, and Plant C can produce up to 4000 units. Warehouse M can handle no more than 5000 units per month, and Warehouse N can handle no more than 4000 units. Retailer W will require 1500 units this month; Retailer x will require 2500 units, Retailer Y will require 1000 units, and retailer z will require 2000 units.
The following charts list the shipping cost ($/100 units) from the plants to the warehouses, and also the shipping cost ($/100 units) from the warehouse to each of the retaliers.
Transportation Costs in $/100 units
From Plant To Warehouse From Warehouse To Retailer
M N W X Y Z
A 7 9
B 9 6 M 4 4 3 5
C 8 4 N 3 2 5 3
Note: The units must be shipped in 100 unit blocks. This is true from plant to warehouse and from warehouse to retailer.
Formulate a linear program that will determine least shipping cost. Must have variable definitions, objective function and constraints