The relationship between the price of a pair of shoes and the number of pairs of shoes sold by a store can be modeled by the equation R(s)= -6s2 + 480s, where R(s) represents the number of shoes sold and s represents the price of a pair of shoes, in dollars. According to this formula, what price should the store set for the pairs of shoes in order to maximize sales? (A) 35(B) 40(C) 55(D) 75
Question
The relationship between the price of a pair of shoes and the number of pairs of shoes sold by a store can be modeled by the equation R(s)= -6s2 + 480s, where R(s) represents the number of shoes sold and s represents the price of a pair of shoes, in dollars. According to this formula, what price should the store set for the pairs of shoes in order to maximize sales? (A) 35(B) 40(C) 55(D) 75
Solution
The equation given is a quadratic equation in the form of y = ax^2 + bx + c, where a = -6, b = 480, and c = 0.
The maximum or minimum of a quadratic equation is given by the formula -b/2a.
Substituting the given values into this formula, we get -480/(2*-6) = 40.
Therefore, the store should set the price of the shoes at $40 to maximize sales. So, the answer is (B) 40.
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