please help - profit/parabola??

[ssjsmom]

the profit (P) in dollars for a company is P=-.001x^2+8x-5000, where x is the number of items produced each month.

a) how many items does the company have to produce to order to obtaim maximum profit?

b) what is the maximum profit?

 

[wjm11]

the profit (P) in dollars for a company is P=-.001x^2+8x-5000, where x is the number of items produced each month.

a) how many items does the company have to produce to order to obtaim maximum profit?

b) what is the maximum profit?

This function is a quadratic, which means it graphs as a parabola. Parabolas extend either upward or downward, depending on the sign of the leading coefficient, in this case -.001. Therefore the parabola opens downward and the function has a maximum at the vertex of the parabola.

 

[galactus]

A non-calc way to find the vertex coordinates is to use \(\displaystyle x=\frac{-b}{2a}\) and

\(\displaystyle y=c-\frac{b^{2}}{4a}\).

'part a' can be answered by using the x coordinate and 'part b' by using the y coordinate of the vertex.