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Problem: A non-linear
pricing model - a case in which sales of products are interdependent.
You manufacture three automobile models,
each with its own price structure and miles-per-gallon rating, at your five plants.
An increase in sales of any one model results in a small decrease in sales of the two
others. The models compete for production capacity in your five plants. Also, the federal
government has imposed an upper limit on the average "fleet mileage" of your
entire production, which makes sales of low-mileage cars more desirable.
You need to set the prices of the three models of automobiles so that profit is maximised
at the five plants, while staying within the federal fleet gas mileage requirement of 24
miles per gallon.
Your known values are the cost of manufacturing each model at each plant, the miles per
gallon for each model, and the annual production capacity at each plant.
You also know price-quantity relationships among the models, called demand curves by
economists. These demands are dependent upon the price of each car related to the prices
of the other cars.
The objective is to determine best price for each car to maximise profit while conforming
to all regulations and constraints.
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