The profit function for a certain company making and selling $x$ units of a product is given by $P ( x ) = - x ^ { 2 } + 16.37 x + 52.44$. Find the smallest value of $x$ at which the company breaks even.
A) $4.37$
B) $\quad 4.21$
C) $\quad 5.21$
D) $\quad 4.69$
E) $\quad 4.94$

Question

Quizplus · Accepted Answer

To find the break-even point, set the profit function $P(x) = 0$ and solve for $x$. Thus, we have $-x^2 + 16.37x + 52.44 = 0$. Solving this quadratic equation for $x$, we find the values of $x$ that make the profit zero. The smallest value of $x$ that satisfies this equation and represents a break-even point is $4.37$.

The Profit Function for a Certain Company Making and Selling xxx

The Profit Function for a Certain Company Making and Selling $x$