Cost , Maximum Revenue, Profit - Help needed with formula required

Mar 2018
6
0
Australia
-Fixed costs are given at $1000.
-Variable cost per unit is given by (x+25)
-Selling Price per unit is given by (250-x)

a) determine break even points
b) find maximum revenue
c) Find maximum profit

Total Cost I believe is Variable Cost(x) + Fixed Cost = (x+25)x + 1000 ; Where I am getting confused is the wording of the problem.
So instead should Total Cost be x+25+1000 & linear. I suspect my functions would have to be quadratic as some point since that's what the
current topic is in school.

To find break even point do I have to say Profit which is (Selling price(x)Units )-(total cost)(x)Unit) = 0
would this be ((250-x)x)-((250-x)+1000) = 0 ; then solve for x? - since asks for B.Even Points ie plural.

Maximum revenue is the Vertex of the (250-x)x function?

Thanks for any insights.
 

SlipEternal

MHF Helper
Nov 2010
3,728
1,571
-Fixed costs are given at $1000.
-Variable cost per unit is given by (x+25)
-Selling Price per unit is given by (250-x)

a) determine break even points
b) find maximum revenue
c) Find maximum profit

Total Cost I believe is Variable Cost(x) + Fixed Cost = (x+25)x + 1000 ; Where I am getting confused is the wording of the problem.
So instead should Total Cost be x+25+1000 & linear. I suspect my functions would have to be quadratic as some point since that's what the
current topic is in school.

To find break even point do I have to say Profit which is (Selling price(x)Units )-(total cost)(x)Unit) = 0
would this be ((250-x)x)-((250-x)+1000) = 0 ; then solve for x? - since asks for B.Even Points ie plural.

Maximum revenue is the Vertex of the (250-x)x function?

Thanks for any insights.
For Total Cost, yes. $(x+25)x+1000$ does not equal $x+25+1000$. You dropped an $x$.

$(x+25)x+1000 = x^2+25x+1000$

Then, the break even point is when $(250-x)x-(x^2+25x+1000) = 0$ which becomes $225x-2x^2-1000 = 0$ or $2x^2-225x+1000 = 0$

For (b), the maximum revenue is as you said.
For (c), the maximum profit is the maximum of $225x-2x^2-1000$ (the formula you used for the break-even points, but not setting it equal to zero).

Do you know how to complete the square?
 
Mar 2018
6
0
Australia
Hello Thanks for the reply... I'm all good with completing the square. :)

Appreciate the help.