Typically, the sales volume declines with an increase of a product price. It has
ID: 3052449 • Letter: T
Question
Typically, the sales volume declines with an increase of a product price. It has been observed, however, that for some luxury goods the sales volume may increase when the price increases. The following Excel output illustrates this rather unusual relationship. Scatterplot of Price Vs Sales for a Luxury Good 2500 4.3224.. 1637 6 R 00012 2000 y0.2702-57.463+4212 0.799 y00007+003522-34581x+3539 1500 Scatterplot of price Vs Sales for Luxury Good Linear(Scatterplot of Price Vs Sales 1000 for o Luxury Good) Poly.(5 catterplot of Price Vs Sales for a Luxury Good -Poly (Scrteplot of Price vs Sales for S0 100 150 200 For which of the following prices do sales predicted by the quadratic regression equation reach their minimum? O 106.33 115716 O 100.41 1166.64Explanation / Answer
Solution
Quadratic equation = f(x) = 0.2702x2 - 57.463x +4212.3
derivative of the equation to get the minimum point
f'(x) = 2(0.2702)x = 57.463 i.e. x = 106.33
minimum value = 0.2702(106.33)2 - 57.463(106.33)+4212.3 = 1157.16 (answer)
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