The relationship between the price of a shirt and the number of shirts sold by a store can be modeled by the equation R(s)= -4s2 + 200s, where R(s) represents the number of shirts sold and s represents the price of a shirt, in dollars. According to this formula, what price should the store set for the shirts in order to maximize sales? (A) 25(B) 35(C) 50(D) 65
Question
The relationship between the price of a shirt and the number of shirts sold by a store can be modeled by the equation R(s)= -4s2 + 200s, where R(s) represents the number of shirts sold and s represents the price of a shirt, in dollars. According to this formula, what price should the store set for the shirts in order to maximize sales? (A) 25(B) 35(C) 50(D) 65
Solution
The equation given is a quadratic equation in the form of y = ax^2 + bx + c, where a = -4, b = 200, and c = 0.
The maximum or minimum of a quadratic equation is given by the vertex of the parabola. The x-coordinate of the vertex can be found using the formula -b/2a.
Substituting the given values into this formula, we get -200/(2*-4) = 25.
Therefore, the store should set the price of the shirts at $25 in order to maximize sales. So, the answer is (A) 25.
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