Please do the calculation with the formulas:

Three employees in the maintenance department are responsible for repairing the video games at Pinball Wizard, a video arcade. A maintenance worker can fix one video game machine every eight hours on average, with an exponential distribution. An average of one video game fails every three hours, according to a Poisson distribution. Each down machine costs the Wizard $$10$ per hour in lost income. A new maintenance worker would cost $$8$ per hour.

$1.$ Should the manager hire any new personnel?

$2.$ If so$,$ how many?

$3.$ What would you recommend to the manager, based on your analysis?