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!

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

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