Question 285707: Report #4
Youth Sports League
A local non-profit youth soccer league is being formed. The coaches will be volunteers, but the league will have to pay $48 per game to cover the cost of the field and referees. At the end of the season, every player will receive an individual trophy, with the league champions receiving special individual trophies as well as a team championship trophy. The league will have to charge each participant enough to cover a proportional share of these expenses.
The proposed format for the league is to have teams of 15 players, with each team playing every other team twice. The league organizers have determined that the demand for the league (i.e., the number of players N wanting to participate) depends on r, the cost per game to play. If the league were free then 312 area children would like to join. However, the number of potential players would drop by thirty for each $1 per game the league had to charge. The league organizers would like to have as many kids participating as possible. If each team is to have 15 players, how much should the league charge each participant for the season?
• Let x be the number of teams in the league.
• What is N in terms of x?
• Express N in terms of r.
• What is r in terms of x?
• In terms of x, how many games g will each team play?
• If p represents the total cost to each participant, what is p in terms of r and g?
• Express p in terms of x.
• Express the league’s revenue R as a function of x.
The team trophy costs $32. The winners’ individual trophies cost $9 each, while the other individual trophies cost $4 each. Express the trophy cost T as a function of x.
How many total games will need to be scheduled (and paid for)? Express the cost C for the field and referees as a function of x.
Express the net income I for the league as a polynomial function in x. Discuss the key aspects of the equation as they relate to the graph of I. Answer by richwmiller(15954) (Show Source):
You can put this solution on YOUR website! Just curious.
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