The two power stations in Problem $1$ have been retrofitted with new

generation technology. Rather than simply being able to operate at $100$MW$,50$MW$,$ or $0$MW and $100$MW or $0$MW$,$ respectively, they can now produce power at any number of

MWs between $100$MW and $0$MW$.$ The hourly production of Power Station $1$ normally

distributed with a mean of $75$MW and a standard deviation of $5$MW$.$ The hourly production

of Power Station $2$ is normally distributed with a mean of $65$MW and a standard deviation of

$10$MW$.$ Line A and Line B have uniformly distributed, independent up times of $87\%$ and

$78\%,$ respectively.

$($a$)$ What is the expected number of MW$-$hours that will be delivered to the load over a

standard year?