Question

A clothing designer determines that the number of shirts she can sell is given by the formula S = −4x2 + 80x − 76, where x is the price of the shirts in dollars. At what price will the designer sell the maximum number of shirts? a $324 b $19 c $10 d $1

Answer 1

To find the price at which the designer will sell the maximum number of shirts, we need to determine the vertex of the quadratic function representing the number of shirts sold.

The equation for the number of shirts sold is given by:

S = -4x^2 + 80x - 76

This is a quadratic function in the form of:

S = ax^2 + bx + c

To find the price at which the maximum number of shirts is sold, we need to locate the vertex of the quadratic function. The x-coordinate of the vertex can be found using the formula:

x = -b / (2a)

In this case, a = -4 and b = 80. Plugging in these values, we can calculate the x-coordinate:

x = -80 / (2*(-4))

x = -80 / (-8)

x = 10

Therefore, the designer will sell the maximum number of shirts at a price of $10. Hence, the correct option is c) $10.