math
posted by Mike on .
Suppose the cost of producing x items is given by C(x)=1000x^3, and the revenue made on the sale of xitems is R(x)=100x10x^2. Find the number of items which serves as a breakeven point.

Break even point is when cost equals revenue (i.e. zero profit).
So for
C(x)=R(x), we have
1000x^3=100x10x^2
Rearrange to give
x^3+10x^2100x+10x^2+1000=0
which solves easily to
x=10