Every home football game for the past $8$ years at Eastern State University has been sold out.

The revenues from ticket sales are significant, but the sale of food, beverages, and souvenirs has contributed greatly to the overall profitability of the football program.

One particular souvenir is the football program for each game. The following probability distribution describes the number of programs sold at each game:

Historically, Eastern has sold between $2,175$ and $2,850$ programs in one game. Each program costs $$0\mathrm{.}75$ to produce and sells for $$2\mathrm{.}00.$

Any programs not sold are donated to a recycling center and do not produce any revenue.

$($a$)$ Simulate the sales of programs at ten football games. Use the last column in the random number table $($Table $13\mathrm{.}4)$ and begin at the top of the column.

$($b$)$ If the university decided to print $2,500$ programs for each game, what would the average profits be for the ten games simulated in part $($a$)?$

$($c$)$ If the university decided to print $2,600$ programs for each game, what would the average profits be for the ten games simulated in part $($a$)?$