MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
A company’s total revenue R(q), measured in dollars, from the sale of q units of a specialty product is modeled for q>0 by
R(q)=q25−10q−1+C,
where C is a constant representing fixed online advertising revenue unrelated to unit sales.
(a) Compute R′(q) and interpret its practical meaning in this context.
(b) For 0<q<10, determine all critical values of R and classify each as giving a local maximum, local minimum, or neither. Show all reasoning.
(c) On what interval(s) of q in 0<q<10 is the total revenue increasing? Justify your answer analytically.
(d) Management wishes to maintain production levels where marginal revenue is at least 15 dollars per unit. Determine the set of q values in the interval 0<q<10 that satisfy this requirement and explain how you arrived at your conclusion.