Thread: 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?

Answer:
a) Find the point of diminishing returns of this model: p(t) = 7.6 (.35)85.5e^(.35t)/(1+7.6e^(-.35t))^2 +10 Max Intersect is at 5.617 b) What does the point of diminishing returns, in this case, tell us? After 5.617 hours you will learn less per hour than previously, this where you are learning the most.


Question:
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