The Martin$-$Beck Company operates a plant in St$.$ Louis with an annual capacity of $30,000$ units. Product is shipped to regional distribution centers located in Boston, Atlanta, and Houston. Because of an anticipated increase in demand, Martin$-$Beck plans to increase capacity by constructing a new plant in one or more of the following cities: Detroit, Toledo, Denver, or Kansas City. The estimated annual fixed cost and the annual capacity for the four proposed plants are as follows:

Proposed Plant Annual Fixed Cost Annual Capacity

Detroit $$175,00040,000$

Toledo $$300,00010,000$

Denver $$375,00020,000$

Kansas City $$500,00030,000$

The company$$s long$-$range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows:

Distribution Center Annual Demand

Boston $20,000$

Atlanta $30,000$

Houston $20,000$