A small company produces and sells x widgets per week. Their cost function in dollars in C(x)=50+3x and their revenue function in dollars is R(x)=(6x-x²)
How many widgets per week should be produced for maximum profit?
(FYI. A widget is "a gadget" or "an unnamed or hypothetical manufactured article">)
I see you've posted a bunch of problems. I personally don't like to answer problems in bulk like this when I don't see you've tried to answer them. For the other posts, maybe you could show some work to help us out. ;)
So the profit (assuming we make more money than we lose) is revenue - cost.
So we have
Using the given functions this comes out to [tex](6x^2-x^3)-(50+3x^2)]/math]. Now differentiate and set it equal to zero to find a max.