(a) A company sells air conditioners. The annual demand for air conditioners is as follows: East, 100,000; South, 150,000; North, 110,000; and West, 90,000. The company is considering building the air conditioners in four different cities (City 1, City 2, City3, and City 4). The variable cost of producing an air conditioner in a city and shipping it to a region of the country is given in the following table.

Unit variable cost ()

East South North West

City 1 206 225 230 290

City 2 225 206 221 270

City 3 230 221 208 262

City 4 290 270 262 215

Any factory can produce up to 150,000 air conditioners annually.

Formulate a linear programming (LP) model to assist the company in minimising the annual variable cost of meeting demand for air conditioners. Solve using appropriate software. Describe your results.

(b) The annual fixed cost of operating a factory in each city is shown in the following table.

City Annual fixed cost ( million)

City 1 6

City 2 5.5

City 3 5.8

City 4 6.2

Revise your formulation to minimise the annual total (variable + fixed) cost of meeting demand for air conditioners. Solve using appropriate software