Question: Suppose the demand for large pepperoni pizza from The Pizza Palace during weekends when there are home football games can be modeled by \(D\left( p \right)=1346\left( {{0.91}^{P}} \right)\) pepperoni pizzas when the price is p dollars per pizza. Due to the limited number of student employees, oven space and delivery drivers, the Pizza Palace can supply large pepperoni pizzas at $p each when there are home games according to the function

\[S\left( p \right)=\left\{ \begin{aligned} & 0\ \text{ }\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{ pizzas when p6} \\ & \text{5}\text{.2}{{\text{p}}^{2}}-50p+190.97\,\,\,\,\,\,pizzas\,\,when\,\,p\ge 6 \\ \end{aligned} \right.\]

where p is the price of a pizza in dollars. Find the social gain at the equilibrium price.