Preference ranking data were obtained from 20 respondents for three brands of dishwashers: X, Y, and Z. Y and Z are existing brands selling for $225 and $175 respectively, while X is a proposed new brand. Table 1 provides the preference ranking data for 3 of the 20 respondents, (i.e., all 3 provided the identical preference ranking indicated in Table 1), Table 2 gives the data for 5 respondents, Table 3 for 4 respondents, and Tables 4 and 5 for 6 and 2 respondents respectively. A rank of 1 indicates the most- preferred product, while 15 indicates the least-preferred product.

a. Compute the proportion of first-place votes for brand X as a function of price when brands Y and Z are at their current prices. (First place is meant in a relative, not absolute sense.)

b. What proportion of first place votes will X receive if its price is $200 while brands Y and Z lower their prices to $200 and $150 respectively?

c. Which brand (Y or Z) suffers the greatest loss in first-place votes with the entry of brand X at $200? 

d. Assume for part (c) that brands Y and Z are selling at their regular price, i.e., $225 and $175 respectively.

	Table 1			Table 2			Table 3			Table 4			Table 5
	X	Y	Z	X	Y	Z	X	Y	Z	X	Y	Z	X	Y	Z
$150 $175 $200 $225 $250	2 4 7 10 13	1 3 6 9 12	5 8 11 14 15	4 5 8 11 13	1 2 3 7 10	6 9 12 14 15	4 6 9 12 15	2 5 8 11 14	1 3 7 10 13	1 2 5 8 11	3 4 7 12 14	6 9 10 13 15	2 5 9 10 15	1 6 8 11 13	3 4 7 12 14