A store has determined that the weekly sales of a product is related to the number of customers who visit the store and the square feet of shelf space, x, according to the following equation: -20x² - 10C² + 40Cx + 120x - 200. C represents the hundreds of customers who visit their store. If a store averages 200 customers per week, how many square feet of shelf space is required to maximize sales? A) 3 B) 4 C) 5 D) 1 or 9

Question

Quizplus · Accepted Answer

To maximize sales, we need to find the vertex of the parabolic equation. We can use the formula x=-b/2a to find the x-coordinate of the vertex. Plugging in the values from the given equation, we get:

x = -40C / (2*(-20))
x = C / 10

Since the store averages 200 customers per week, we can plug in C=2 into the equation and get x=0.2. However, since x represents the square feet of shelf space, the answer needs to be a whole number. The closest whole numbers to 0.2 are 0 and 1. Therefore, the answer is either 1 or 9. However, since we want to maximize sales, we should choose the larger value, which is 9. Therefore, the answer is D) 1 or 9.

A Store Has Determined That the Weekly Sales of a Product