please help solve, thank you

label Calculus
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the total costs for a company =  c (x) = 2000 + 40x +x^2 and total revenue is (x) = 130x.

a. Find break even points

b. what is the maximum profit?

Thank you!

Oct 3rd, 2015

Thank you for the opportunity to help you with your question!

Break even point is when cost is equal to revenue;

x^2+40x+2000=130x

x^2-90x+2000=0

x=40  and  50 (break even points)

.............................................................

Profit=revenue- the total costs=P=130x-x^2-40x-2000=-x^2+90x-2000=-(x-40)(x-50)

For Maximum, dp/dt=-2x+90=0 ;x=45

Thus Profit is -(45-40)(45-50)=25

Final Answer  Break even points are at x=40,50 and profit is 25

Please let me know if you need any clarification. I'm always happy to answer your questions.
Sep 22nd, 2015

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