Question

A company earns P dollars by selling x items, according to the equation P(x)=-0.002x^2+5.5x-1000. How many items does the company have to sell each week to maximize the profit?

Answer 1

so.. check the picture below

that's when the profit gets maximized


`\bf \qquad \textit{vertex of a parabola}\\ \quad \\ \begin{array}{lccclll} P(x)=&-0.002x^2&+5.5x&-1000\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)`

how many items does the company need to sell? they need to sell
`\bf -\cfrac{{{ b}}}{2{{ a}}}`