Word Problem: Maximizing Profit

[cgarcia71]

I have the following word problem and I am trying to figure it out. I have sat down and read it back and forth and this is what I have come up with.

The total profit (in dollars) for sales of x rowing machines is given by P(x) = 0.2x^2 + 300x - 200. What is the profit if 500 are sold? For what value of x will the profit be at a maximum?

x = rowing machines

is P = 500?

I am totally lost. I have finals this week and I think I am going to fail. Can anyone recommend a tutor?

 

[stapel]

If "P" is the profit and the profit is 500, then, yes, P = 500. So plug "500" in for "P" and solve the quadratic equation.

Eliz.

 

[cgarcia71]

Is this correct?

P(x) = 0.2x^2 + 300x - 200

500(x) = 0.2x^2 + 300x - 200

500x -300 x = 0.2x^2 - 200

200x = 0.2x^2 - 200

x = 0.2x^2 - 200
200

x = 0.2x^2

Is this right?

 

[stapel]

Re: Is this correct?

P(x) = 0.2x^2 + 300x - 200

500(x) = 0.2x^2 + 300x - 200

Why are you multiplying P(x) by x? Or are you not familiar with function notation?

And regarding your steps that follow: Are you not familiar with the techniques for solving quadratic equations?

Thank you.

Eliz.

 

[cgarcia71]

Reply to Liz

I am not familiar with either of the methods you mention below. Can you help me understand?

Thank you.