Question

The total revenue R earned per day (in dollars) from a pet-sitting service is given by R(p) = -10p2 + 130p where p is the price charged per pet (in dollars). Find the price that will yield a maximum revenue. $7.5 $6.5 $8.5 $10.5

Answer 1

check the picture below.


`\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{lccclll} R(p) = &{{ -10}}p^2&{{ +130}}p&{{ +0}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right) \\\\\\ \left( -\cfrac{130}{2(-10)}~~,~~0-\cfrac{130^2}{4(-10)} \right)\implies \left( \cfrac{13}{2}~~,~~\cfrac{4225}{10} \right) \\\\\\ \left( \stackrel{price}{6(1)/(2)}~~,~~\stackrel{revenue}{422(1)/(2)} \right)`