# Thread: Diminishing Returns Problem, Revenue Problem

1. ## Diminishing Returns Problem, Revenue Problem

I would greatly appreciate it if I could get some feedback on these Calculus questions. Answer one or all, any help would be appreciated. THANKS!

Question:
The grade, out of 100 pts, of an exam is a function of t, the number of hours of study an average student puts in for that exam: p(t)=85.5/1+7.6e^(-0.35t) +10 points. a) Find the point of diminishing returns of this model: b) What does the point of diminishing returns, in this case, tell us?

The number of DVDs sold weekly at a certain movie store is given by 12350(0.94^x) DVDs, when each DVD is sold at x dollars. a) Find their weekly revenue function when the price is set to x dollars (per DVD): b) What specific price (per DVD) should they set to maximize their weekly revenue? c) If the store pays DVD distributors $9.99 for each DVD, and assume that they sell all DVDs they purchase, at what price should they sell each DVD to maximize their weekly profit? Answer: a) Find their weekly revenue function when the price is set to x dollars (per DVD): N(x) = (x)(12350(0.94^x)) b) What specific price (per DVD) should they set to maximize their weekly revenue? Max= 15.95 dollars per DVD c) If the store pays DVD distributors$9.99 for each DVD, and assume that they sell all DVDs they purchase, at what price should they sell each DVD to maximize their weekly profit? cost + max revenue price 9.99 + 15.95 = 25.94 dollars per DVD for max profit