Southwestern University $($SWU$),$ a large state college in Stephenville, Texas, enrolls close to $20,000$ students. The school is a dominant force in the small city, with more students during fall and spring than permanent residents.

Always a football powerhouse, SWU is usually in the top $20$ in college football rankings. Since the legendary Phil Flamm was hired as its head coach in $2012($in hopes of reaching the elusive number$-$one ranking$),$ attendance at the five Saturday home games each year increased. Prior to Flamm$$s arrival, attendance generally averaged $25,000$ to $29,000$ per game. Season ticket sales bumped up by $10,000$ just with the announcement of the new coach$$s arrival. Stephenville and SWU were ready to move to the big time!

The immediate issue facing SWU, however, was not NCAA ranking. It was capacity. The existing SWU stadium, built in $1953,$ has seating for $54,000$ fans. The table indicates attendance at each game for the past $6$ years.

One of Flamm$$s demands upon joining SWU had been a stadium expansion, or possibly even a new stadium. With attendance increasing, SWU administrators began to face the issue head$-$on$.$ Flamm had wanted dormitories solely for his athletes in the stadium as an additional feature of any expansion.

SWU$$s president, Dr$.$ Joel Wisner, decided it was time for his vice president of development to forecast when the existing stadium would $$max out.$$ The expansion was, in his mind, a given. But Wisner needed to know how long he could wait. He also sought a revenue projection, assuming an average ticket price of $$50$ in $2019$ and a $5\%$ increase each year in future prices.

Discussion Questions

Develop a forecasting model, justifying its selection over other techniques, and project attendance through $2020.$

What revenues are to be expected in $2019$ and $2020?$

Discuss the school$$s options.

Please show me the steps with calculations