What changes would you make to the model in part a so that

Question

RFC Bearings has just entered the U.S .market.  It has three major DCs in the Atlanta, Boston, and Chicago areas.

Annual demand served by each DC is estimated to be:

                                Atlanta 10,000                   Boston 20,000                    Chicago 15,000

Four plants (Memphis, Philadelphia, Toledo) supply the DCs.  Per-unit transportation costs and plant capacities are given in the following table:

Plant Location	Distribution Center			Plant Capacity
	Atlanta	Boston	Chicago
Memphis	$3	9	7	30,000
Philadelphia	5	2	4	35,000
Toledo	6	6	2	35,000

Using the notation:

X_MA = Qty shipped from Memphis to Atlanta

X_MB = Qty shipped from Memphis to Boston, etc.,

write down a model that will determine the optimal demand allocation (i.e. minimize transportation costs.)

Suppose now that the three locations (Memphis, Philadelphia, Toledo) are potential locations, i.e., each plant would only be constructed if it improves overall cost (i.e., transportation plus plant fixed costs).  The data is repeated here with the (annualized) plant fixed costs shown additionally.

Plant Location	Distribution Center			Plant Capacity	Annualized Fixed Costs
	Atlanta	Boston	Chicago
Memphis	$3	9	7	30,000	$50,000
Philadelphia	5	2	4	35,000	45,000
Toledo	6	6	2	35,000	48,000

What changes would you make to the model in part (a) so that we can determine the optimal locations of the plants as well as the optimal demand allocation (i.e. minimize both transportation as well as fixed costs).