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# Computer Shopping

You are considering the purchase of a computer and have consulted several computer magazines that contain ratings and prices for the five models you are investigating. You decide to include price, speed, and expansion capabilities as three criteria on which you will judge the models under consideration. The ratings, with 10 being the highest for speed and expansion, and the prices are summarized in the following table.

Brand Price Speed Rating Expansion Rating
Dell \$1,921 8 10
NEC \$2,020 8 8
Gateway Essential \$1,528 6 6
Compaq \$2,410 10 8
Sony \$2,500 8 6

a.One model dominates a second model if it is better in all criteria than the second model. Do any of the models given in the table dominate another model? If so, which one dominates and which one is dominated? Explain how you would use this information.

b. Change each value in the price column to a relative rating based on a highest rating of 10.

c. Assign a weighting factor to each of the three criteria of price, speed, and expansion to use the weighted sum method for making a decision. Give a justification for your choices.

d. Use your weighting factors to find the weighted sum for each of the five models. Which model would you choose to buy, based on your weighted sum?

e. What other criteria might you want to include before you decide which computer to buy?

#### Solution Preview

a. The Dell dominates the NEC and the Sony, and the Compaq dominates the Sony. This means you shouldn't buy the NEC or the Sony.

b. One way to obtain a price rating (PR) is to perform a linear transformation on the price which maps the price range to the range 0 - 10, with lowest price corresponding to highest rating, and then round the results. Thus, for instance, the Sony would have a PR of 0, Gateway essential a PR of 10, and the price rating over the other three computers ...

#### Solution Summary

We show how to decide what computer to buy by computing a weighted average of various ratings of different models.

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