FlexSteal, marketed as a miracle brush-on sealant and baldness cure, is manufactured at three plants that are struggling to keep up with the demand at the four regional centers. The cost to ship a truckload from each of the existing plants to the regional centers is shown in the table.

	Philadelphia	atlanta	dallas	LA	capacity
plant 1	89	75	93	115	400
plant 2	120	88	103	93	400
plant 3	95	82	112	98	400
total demand	350	350	350	350

The supply chain manager has explored plant construction costs in two other cities as well as the cost to ship a truckload from each of the plants to the regional centers. The current plan is to build another plant with a capacity of 400 to allow room for sales growth. The construction cost for the new plants and cost to ship to each of the regional centers is shown here

	Philadelphia	atlanta	dallas	LA	cost to build
plantA	94	78	95	95	23500
Plant B	95	88	88	94	26000

FlexSteal wants to use LP to decide its supply chain network and which plant they should add in order to minimize the total cost. 

a) Define the decision Variables 

b) Determine the objective function 

c) Determine the constraints