A profit function is derived from the production cost and revenue function for a given item. The monthly profit function for a c

Question

3 years ago

13

A profit function is derived from the production cost and revenue function for a given item. The monthly profit function for a c

ertain item is given by P(x)=−0.05x^2+500x−100,000, where P is in dollars and x is the number of units sold. How many units maximize the profit? FInd the maximum profit

Mathematics

1 answer:

SpyIntel [72] · Answer 1 · 2022-06-03T21:30:29+03:00

SpyIntel [72]3 years ago

5 0

Check the picture below.

$\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\
\begin{array}{lccclll}
P(x) = &{{ -0.05}}x^2&{{ +500}}x&{{ -100000}}\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array}\qquad 
\left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)\\\\
-------------------------------\\\\
\textit{so }-\cfrac{b}{2a}\textit{ units maximize the profit, and}\\\\\\
c-\cfrac{b^2}{4a}\textit{ dollars is the maximum profit}$