Suppose the revenue, in dollars, for producing x chairs is given by r(x)=50x and the cost to produce the chairs is given by c(x)=0.001x^3-0.1x^2+12x+1500. Find the production level that will maximize profit.

Question

nottim · Answer

ehh....i can't help much. by you are suppose to think of the situation as a parabola, no?

accessdenied · Answer

well, it sounds like you're trying to find the x-value that maximizes the profit function.  first step is getting the profit function, which isn't too hard.  you'll also want to identify the restrictions; P(x) > 0 and x>0

accessdenied · Answer

er not P(x) > 0

anonymous · Answer

How do you get the profit function?

accessdenied · Answer

well, profit is the amount you're making after you take out the costs.  Revenue is how much you're making originally.
So, the profit would be "revenue - cost."

anonymous · Answer

Oh haha okay, cool. That makes sense. So if I plug 50x-(0.001x^3-0.1x^2+12x+1500) into my graphing calculator and find my maximum in terms of x, that's my answer?

accessdenied · Answer

yeah, that should be correct
i didnt actually graph it myself, just make sure that the maximum is on x>0

accessdenied · Answer

so, you don't need to use the calculus approach of finding the maxima?  :P

anonymous · Answer

Lol, well ideally I do. But I'm being lazy right now :p