Para encontrarmos o faturamento, realizaremos os cálculos abaixo:

\(\begin{align} & ~R\left( p \right)\text{ }=-\text{ }0,5\text{ }{{p}^{2}}~+\text{ }30p \\ & F=\int_{15}^{30}{R(p)} \\ & F=\int_{15}^{30}{-\text{ }0,5\text{ }{{p}^{2}}~+\text{ }30p} \\ & F=\left[ -\frac{0,5{{p}^{3}}}{3}+\frac{30{{p}^{2}}}{2} \right]_{15}^{30} \\ & F=\left[ -\frac{0,5{{p}^{3}}}{3}+15{{p}^{2}} \right]_{15}^{30} \\ & F=\left[ -\frac{0,5\cdot {{30}^{3}}}{3}+15\cdot {{30}^{2}} \right]-\left[ -\frac{0,5\cdot {{15}^{3}}}{3}+15\cdot {{15}^{2}} \right] \\ & F=7500 \\ & F=\$7500\end{align}\ \)

Portanto, o faturamento será de $7500.