Description
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!
Explanation & Answer
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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