A car dealer specializing in late model used cars collected the following data on the selling price and mileage of five cars of the same make and model year at an auto auction:

Mileage Price

43,890 ..........$12,500

35,750 ..........$13,350

27,300 ..........$14,600

15,500 ..........$15,750

8,900 .........$17,500

Because there seems to be a strong relationship between mileage and price, the dealer wants to use this information to predict this type of car’s market value on the basis of its mileage. The dealer thinks that the car’s selling price can be predicted as:

Estimated price = A + B × mileage

A and B represent numeric constants (which might be positive or negative). Using the data collected at last week’s auction, the dealer wants to determine appropriate values for A and B that minimize the following quantity:

This objective seeks to find values of A and B that minimize the sum of the absolute value of the deviations between the actual prices of the cars and the estimated prices.
a. Create an LP model using deviational variables whose solution provides the best values for A and B using the stated criteria. That is, what values of A and B minimize the sum of the absolute deviations between the actual and estimated selling prices?
b. Implement your model in a spreadsheet and solve it.
c. Using the values of A and B determined by your solution, what should the estimated selling price be for eachcar?

Transcribed Image Text:

MIN: IA + B × 43890-125001 + IA + B × 35750-133501 + IA + B × 27300-14600| + IA + B × 15500-157501 + IA + B × 8900-175001