Chapter 5.2, Problem 78E

Price–supply equation. The marginal price at a supply level of x bottles of laundry detergent per week is given by

     $p^{\prime }\left(x\right)=\frac{300}{{\left(3x+25\right)}^2}$

Find the price–supply equation if the distributor of the detergent is willing to supply 75 bottles a week at a price of $5.00 per bottle. How many bottles would the supplier be willing to supply at a price of $5.15 per bottle?