The revenue R (in dollars)for selling x units of an infant stroller is modelled by $R = x \left( 50 - \frac { 1 } { 4 } x \right) , 0

Question

The revenue R (in dollars)for selling x units of an infant stroller is modelled by $R = x \left( 50 - \frac { 1 } { 4 } x \right) , 0 < x < 100$ . Find the number of strollers that must be sold to produce a revenue of $2176 . Round your answer to the nearest integer.
A) 26 strollers
B) 64 strollers
C) 45 strollers
D) 32 strollers
E) $43$ strollers

Quizplus · Accepted Answer

To find the number of strollers, solve the equation $R = x \left( 50 - \frac{1}{4} x \right) = 2176$. Simplifying gives $50x - \frac{1}{4}x^2 = 2176$. Multiply through by 4 to clear the fraction: $200x - x^2 = 8704$. Rearrange to form a quadratic equation: $x^2 - 200x + 8704 = 0$. Solving this quadratic equation using the quadratic formula gives two solutions, one of which is approximately 64.

The Revenue R (In Dollars)for Selling X Units of an Infant