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).

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26 August, 19:55

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).

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Elliot · 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).

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.