Lane Manufacturing estimates that its weekly profit, P, in thousands of dollars, can be approximated by the formula P = -0.1x2 + 0.6x + 3 where x is the number of units produced per week, in thousands.
a. How many units should the company produce per week to earn the maximum profit?

Question

Lane Manufacturing estimates that its weekly profit, P, in thousands of dollars, can be approximated by the formula P = -0.1x2 + 0.6x + 3 where x is the number of units produced per week, in thousands.
a. How many units should the company produce per week to earn the maximum profit?

tlynne16 · Answer

@Mehek14

fwizbang · Answer

You could rewrite the equation as P=a(x-h)^2+k. Can you find a,h, and k?
(I'm assuming this is an algebra question, not calculus)

photon336 · Answer

@Tlynne16 can you use calculus for this or not? it's pretty  straightforward that way.  

Hey @fwizbang how would we go about finding the maximum value? 

$$P = a(x-h)^{2}+k $$

fwizbang · Answer

If a<0, then P has a maximum at h=k.

fwizbang · Answer

err...x=h.

tlynne16 · Answer

what is the easiest way to find this?

tlynne16 · Answer

it is an algebra question

fwizbang · Answer

So, if p=a(x-h)^2+k, then P= ax^2-2ahx +ah^2+k. Compare this to your equation. Whatever multiplies x^2 is a, whatever multiplies x is -2ah. So,

a=?
-2ah=?

tlynne16 · Answer

I am so confused.

photon336 · Answer

@Tlynne16 try to compare coefficients

fwizbang · Answer

The equation you are given is $$P=-0.1x^2+6x+3$$

In this equation, what multiplies $$x^2$$?