# Math Help - Case Problem

1. ## Case Problem

The Valley Swim Club has 300 stockholders, each holding one share of stock in the club. A share of club stock allows the shareholder's family to use the club's heated outdoor pool during the summer upon payment of annual membership dues of $175. The club has not issued any new stock in years, and only a few of the existing shares come up for sale each year. The board of directors administers the sale of all stock. When a share*holder wants to sell, he or she turns the stock into the board, which sells it to the person at the top of the waiting list. For the past few years, the length of the waiting list has remained relatively steady at approximately 20 names. However, during the past winter two events occurred that have suddenly increased the demand for shares in the club. The winter was especially severe, and subzero weather and heavy ice storms caused both the town and the county pools to buckle and crack. The problems were not discovered until maintenance crews began to ready the pools for the summer, and repairs cannot be completed until the tall. Also during the winter, the manager of the local coun*try club had an argument with her board of directors and one night burned down the clubhouse. Although the pool itself was not dam*aged, the dressing room facilities, showers, and snack bar were destroyed. As a result of these two events, the Valley Swim Club was inundated with applications to purchase shares. The waiting list suddenly grew to 250 people as the summer approached. The board of directors of the swim club had refrained from issuing new shares in the past because there never was a very great demand, and the demand that did exist was usually absorbed within a year by stock turnover. Inaddition, the board has a real concern about overcrowding. It seemed like the present member*ship was about right, and there were very few complaints about overcrowding, except on holidays like Memorial Day and the Fourth of July. However, at a recent board meeting a number of new applicants had attended and asked the board to issue new shares. In addition, a number of current shareholders suggested that this might be an opportunity for the club to raise some capi*tal for needed repairs and to improve some of the existing facili*ties. This was tempting to the board. Although it had set the share price at$500 in the past, the board could set it at a much higher level now. In addition, any new shares sold would result in almost total profit since the manager, lifeguards, and maintenance costs had already been budgeted for the summer and would not increase with additional members.

Before the board of directors could make a decision on whether to sell more shares and, if so, how many, the board members felt they needed more information. Specifically, they would like to know the average number of people (family members, guests, etc.) that might use the pool each day during the summer. They would also like to know the number of days they could expect over 500 people to use the pool from June through August, given their current number of shares.

The board of directors has the following daily attendance records for June through August from the previous summer; it thinks the figures would provide accurate estimates for the upcoming summer.

1. The expected number of days where attendance would exceed 500 should be no more than five with the current membership.

2. The current average daily attendance is no more than 320.

3. The average daily weekend (Saturday and Sunday) atten*dance is no more than 500. (Weekend attendance is every sixth and seventh entry in each progression of seven entries in the preceding data.)

If these criteria are met, the club will issue one new share at a price of \$1,000 for every two average attendees between the cur*rent daily average and an upper limit of 400.

Should the club issue new shares? If so, how many will it issue, and how much additional revenue will it realize?

I have attached the data file with this.

Appreciate any help to solve this problem.