I need help!

[waterloo699]

i have a calc problem :

For a certain product, the cost function is C(x)= 25+3x+x^3, and the demand function is P(x)= 40 - 0.1x. Determine the prouction level that maximizes profit.

 

[Unco]

Let R(x) be the profit function; assume x to be production level.

Profit = Demand - Cost

R(x) = P(x) - C(x)

R(x) = (40 - 0.1x) - (25 + 3x + x^3)

Simplify. Differentiate. Set to zero. Solve for x.

At the moment there is real solution to R'(x)=0, so as we aren't given a domain to test endpoints, maybe a typo?