Profit and Cost: R(x)=25x-0.01x^2 C(x)=4x-20; Determine the profit function P(x)

[prenzulli]

Hello All I am very confused with the following problem. If someone could help me with this I would greatly appreciate it.

R(x)=25x-0.01x^2 C(x)=4x-20
Determine the profit function P(x)
I got -0.01x^2+21x+20
Find the number of units that must be sold to maximize profit as well as max profit
Units I got 1050 and Max profit i got $11045
Lastly I need to find the number of units needed in order to break even and Im lost. Can someone please check and make sure it is correct I feel like I'm doing it all wrong. Thank You!

 

[Deleted member 4993]

Hello All I am very confused with the following problem. If someone could help me with this I would greatly appreciate it.

R(x)=25x-0.01x^2 C(x)=4x-20
Determine the profit function P(x)
I got -0.01x^2+21x+20
Find the number of units that must be sold to maximize profit as well as max profit
Units I got 1050 and Max profit i got $11045
Lastly I need to find the number of units needed in order to break even and Im lost. Can someone please check and make sure it is correct I feel like I'm doing it all wrong. Thank You!

Can you please tell us the definition of the Breakeven number?

 

[stapel]

Hello All I am very confused with the following problem. If someone could help me with this I would greatly appreciate it.

R(x)=25x-0.01x^2 C(x)=4x-20
Determine the profit function P(x)

I will guess that "R(x)" is the "revenue" function, in terms of units "x" sold; that "C(x)" is the cost function, in terms of units "x" produced; that "P(x)" is the "profit" function, in terms of units "x" sold; and that you're supposed to assume that all units produced are then successfully sold.

I got -0.01x^2+21x+20

You don't show your steps. I will assume that you applied the definition of "profit", in terms of revenues and costs, as did the following:

. . . . .\(\displaystyle \begin{align} P(x)\, =\, R(x)\, -\, C(x)\, &=\, \left(25x\, -\, 0.01x^2\right)\, -\, \left(4x\, -\, 20\right)\

\\ \\ &=\, 25x\, -\, 0.01x^2\, -\, 4x\, +\, 20

\\ \\ &=\, -0.01x^2\, +\, 25x\, -\, 4x\, +\, 20

\\ \\ &=\, -0.01x^2\, +\, 21x\, +\, 20 \end{align}\)

Find the number of units that must be sold to maximize profit as well as max profit
Units I got 1050 and Max profit i got $11045

I will guess that you applied some method (?) to find the vertex of the parabola.

Lastly I need to find the number of units needed in order to break even and Im lost. Can someone please check and make sure it is correct I feel like I'm doing it all wrong.

Since you haven't show your work for finding the break-even point, there is no way for us to check it. Sorry. Please reply showing your book's definition of "break-even point", and how you applied this definition to the functions R(x) and C(x) (or P(x), if that's how your book defines things). Thank you!

 

[Harry_the_cat]

Hello All I am very confused with the following problem. If someone could help me with this I would greatly appreciate it.

R(x)=25x-0.01x^2 C(x)=4x-20
Determine the profit function P(x)
I got -0.01x^2+21x+20
Find the number of units that must be sold to maximize profit as well as max profit
Units I got 1050 and Max profit i got $11045
Lastly I need to find the number of units needed in order to break even and Im lost. Can someone please check and make sure it is correct I feel like I'm doing it all wrong. Thank You!

Yes Profit = Revenue - Cost .... so your profit function is correct.

The max turning point is (1050, 11045) so you've got the answers correct there. (Although since you don't show any working or explain how you got those answers, I have no way of knowing if your method was correct).

Check your book, but I assume that "breakeven" means Revenue = Cost, ie. Profit = 0. Can you proceed from there?