7. A garage band wants to hold a concert. The expected crowd is 3,000. The average expenditure on concessions is $15. Tickets sell for $10 each, and the band’s profit is 80% of the gate and concession sales, mi- nus a fixed cost of $12,000. Develop a general mathematical model and implement it on a spreadsheet to find their expected profit.

9. For a new product, sales volume in the first year is estimated to be 80,000 units and is projected to grow at a rate of 4% per year. The selling price is $12 and will increase by $0.50 each year. Per-unit variable costs are $3, and annual fixed costs are $400,000. Per-unit costs are expected to increase 5% per year. Fixed costs are expected to increase 8% per year. Develop a spreadsheet model to calculate the net present value of profit over a 3-year period, assuming a 4% discount rate.

A stockbroker calls on potential clients from referrals. For each call, there is a 10% chance that the client will decide to invest with the firm. Fifty-five percent of those interested are found not to be qualified, based on the brokerage firm’s screening criteria. The remaining are qualified. Of these, half will invest an average of $5,000, 25% will invest an average of $20,000, 15% will invest an average of $50,000, and the remainder will invest $100,000. The commission schedule is as follows:

Transaction Amount | Commission |

Up to 25,000 | $50 + 0.5% of the amount |

$25,001 to $50,000 | $75 + 0.4% of the amount |

$50,001 to $100,000 | $125 + 0.3% of the amount |

The broker keeps half the commission. Develop a spreadsheet to calculate the broker’s commission based on the number of calls per month made. What is the expected commission based on making 600 calls?

**Chapter 12**

3. A professional football team is preparing its budget for the next year. One component of the budget is the revenue that they can expect from ticket sales. The home venue, Dylan Stadium, has five different seating zones with different prices. Key information is given below. The demands are all assumed to be normally distributed.

Seating Zone | Seats Available | Ticket Price | Mean Demand | Standard Deviation |

First Level Sideline | 15,000 | $100.00 | 14,500 | 750 |

Second Level | 5,000 | $90.00 | 4,750 | 500 |

First Level End Zone | 10,000 | $80.00 | 9,000 | 1,250 |

Third Level Sideline | 21,000 | $70.00 | 17,000 | 2,500 |

Third Level End Zone | 14,000 | $60.00 | 8,000 | 3,000 |

Determine the distribution of total revenue under these assumptions using an Excel data table with 50 simulated trials. Summarize your results with a histogram.