Cars sold, N Dealership Rank (1, 1280) (4, 1323) (13, 158) (12, 116) Figure 1: Scatter plot of the number of cars sold (N) by a dealership and the dealership rank. Data were obtained from the article by Fahey in a recent issue of Forbes magazine (June 21, 2004, page 70). The highest number of cars were sold by the Toyota dealership, with rank 4. The top ranked Lexus dealership sold slightly lower number of cars. Likewise, slightly higher number of cars were sold by the lowest ranked Chrysler dealership (rank 13) compared to the Lincoln dealership (rank 12). © 2004 /vlaxmanan/Charmed/VJLCov ePostPrft1.ppt/26DEC04

Planck number P P = -126.1x + 1801.4 Dealership Rank (1, 2385) (2, 1549) P = -126.1x + 1801.4 (13, 162) Figure 2: A nice linear trend is observed when the Planck number P is plotted against the dealership rank. The Planck number P is obtained using the relation NM = P where M is the “average” price per car sold by the dealership and N is the number of cars sold. The product NM is the total sales revenue. This product can also be written as P where  is the average price per car sold by a dealership which is being used as a reference body, similar to reference bodies (water, light) used in physics. The (N, M) data were obtained from the article by Fahey in a recent issue of Forbes magazine (June 21, 2004, page 70). The linear trend can be described by the equation P = - 126.1x + 1801.4 where x is the dealership rank. The top ranked Lexus dealership falls above this trend line. The slope of the line is fixed by considering the two dealerships ranked 2 and 13, the two extreme points on the graph. Thus, (1549 - 162)/(2 - 13) = - 126.1 and the intercept equals 1801.4. © 2004 /vlaxmanan/Charmed/VJLCov ePostPrft1.ppt/26DEC04

Selling price per unit, M Units sold per dealership, N Mercedes Benz Lexus Toyota Jaguar Infiniti Figure 3: Graphical representation of the sales data for the 13 dealerships. There is obviously no clear relationship between the number of units sold and the average selling price of the cars sold by these dealerships. The Jaguar and the Lexus have nearly the same selling price but the units sold are very different. Mercedes Benz, with a higher selling price, sold more units. Lexus and Toyota, with the two brands with the highest units sold, have an average selling price that is higher than the selling price for some of the other cars sold. © 2004 /vlaxmanan/Charmed/VJLCov ePostPrft2.ppt/27DEC04

Actual units sold per dealership, N y = 42.5x Lexus Toyota M. Benz Jaguar y = 42.5x Revenues MN = NM [$, millions] Infiniti Chrysler Honda Figure 4: Graphical representation of the sales revenue data for the 13 dealerships. At a fixed selling price, the sales revenues increase as the number of units sold N increases. However, there is some scatter in the data and this is clearly due to the large variations in the average selling price per unit sold at each of the 13 dealerships. The slope of the straight line passing through the origin and the Lexus data point is equal to the average selling price for a Lexus. Hence, the equation of the straight line superimposed on this graph is y = 42.5x where y is sales revenues (in $, millions) and x is the units sold. Notice that the data point for Jaguar falls very nearly on this line since the selling price is the same. The revenues are lower since the number of units sold is lower. © 2004 /vlaxmanan/Charmed/VJLCov ePostPrft2.ppt/27DEC04

Revenues MN = P [$, millions] y = 23x Planck Number P (hypothetical units) Figure 5: Graphical representation of the sales data for the 13 dealerships. The Planck number P may be thought of as the hypothetical number of units sold by each dealership (to attain the same revenues), using the average selling price for the Toyota as the “reference”. The sales revenues increases perfectly linearly with increasing P. The slope of the straight line is the “quantum” of money. The equation of the straight line is y = 23 x where x = P is the hypothetical units sold and y is sales revenues in millions of dollars. © 2004 /vlaxmanan/Charmed/VJLCov ePostPrft2.ppt/27DEC04