Assist me in answering the two highlighted questions below:

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 detroit toledo denver kansas city annual fixed cost $175,000 $300,000 $375,000 $500,000 annual capacity 30,000 40,000 10,000 20,000

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

(a) develop a mixed-integer programming model that could be used to martin- beck determine which new plant or plants to open in order to satisfy anticipated demand. solve the model and answer the following questions. what is the optimal cost?

(12.1 equation)

step 1: solve the original problem

step 2: create two sets:

o = the set of variables equal to one in step 1

z = the set of variables equal to zero in step 1

step 3: add the following constraint to the original problem, and solve

(sum of variables in the set o) - (sum of variables in the set z) < (number of variables in the set o) - 1