DryIce Inc. faces the tradeoff between fixed cost $($that is lower per item in a larger plant$)$

versus the cost of shipping and manufacturing. The typical scenarios that need to be

considered are either having regional manufacturing if the shipping costs are significant or

have a centralized facility if the fixed costs show significant economies to scale.

We keep the units shipped from each plant to every region as variable and choose the fixed

cost based on the emerging production quantities in each plant location. The total system

cost is then minimized with the following constraints:

a$.$ All shipment numbers need to be positive integers.

b$.$ The maximum production capacity is $400,000.$

c$.$ All shipments to a region should add up to the requirement