Question

A manufacturer produces bolts of fabric with a fixed width. The quantity q of this fabric (measured in yards) that is sold is a function of the selling price p (in dollars per yard), so we can write q = f(p). Then the total revenue earned with selling price p is R(p) = pf(p). Given f(16) = 8000 and f '(16) = -330, find R'(16).

Answer 1

This means that the total revenue of the manufacturer, when he is selling the fabric at $16, is going up by 5,600(which, of course,is good).

Step-by-step explanation:

The derivative of R(p) is R'(p)=f(p)+pf '(p). So for the values given before, R(16)=8,000+(16)(-350)=8,000-7,000=5,600. This means that the total revenue of the manufacturer, when he is selling the fabric at $16, is going up by 5,600(which, of course,is good).

Note how, even though the amount being sold is going down, therevenue is going up.