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# A manufacturer produces bolts of a 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 $R(p) = pf(p)$.(a) What does it mean to say that $f (20) = 10,000$ and $f'(20) = - 350?$(b) Assuming the values in part (a), find $R'(20)$ and interpretyour answer.

## (a) See explanation(b) $R^{\prime}(20)=3000$

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##### Kristen K.

University of Michigan - Ann Arbor

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he excludes the one you radio. So for part A, we have two interpretations. The 1st 1 which is up 20 equals 10,000 says that if the price is $20 in 10,000 units will be sold for the derivative of 20 equals Negative. 3 50 means that increasing the selling price by$1 will decrease sails by 350 units. For Part B. We're going to do a calculation. So first we're going to have our of P equal. P times are 50. We differentiate our we get P terms, the derivative of of P less one times of p. We plug in 20 when we get the derivative of 20 equal to 20 times negative 3 50 plus one terms, 10,000 just equal to 300 3000 excusable. And since it's positive means that increasing the selling price will increase the revenue

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