Problem $96.$ Price$-$supply equation. According $to$ economic theory, the supply $xof$ a quantity

$in$ a free market increases $as$ the price $p$ increases. Suppose that the number $xofDVD$ players $a$

retail chain $is$ willing $to$ sell per week $at$ a price $of$ $$pis$ given $by$

$x=\frac{100p}{0\mathrm{.}1p+1},10p70$

$(A)$ Find $\frac{dx}{dp}$

$(B)$ Find the supply and the instantaneous rate $of$ change $of$ supply with respect $to$ price when

the price $is$ $$40.$ Write a brief verbal interpretation $of$ these results.

$(C)$ Use the results from part $(B)to$ estimate the supply $if$ the price $is$ increased $to$ $$41.$