Part 1

A school principal has to schedule buses for students who live in the suburbs. 30 students can use each bus. Records from past years indicate the demand for buses follows a normal distribution with a mean of 2500 and a standard deviation of 250.

Operating costs per bus per month follows a uniform distribution with a minimum of $400 and a maximum of $600. Students in the suburbs currently each pay a $15 dollar per month transportation fee. Remember there can be no fractional buses. Build a model of this situation.

a. What is the probability the current transportation fee will cover the cost of operating the buses?

b. What is the probability the montthly operating loss will exceed $2500?

c. What is the probability the operating loss will between $(1000) and $(5000)?

d. If the principal wants to be 50% certain the bus system will break even, approximately what monthy transportation fee should he charge?

Note: Just use your judgement and re-run the simulation with a few different transportation fees - no need to use Solver to optimize.

Part 2

Charlie Company sells virtual reality headsets and is expecting rapid growth. To convince angels to invest $1,000,000, they need to show consistent profits and growth for the next five years. They used the Delphi Method to build their forecasts, but there are risks and uncertainties they need to understand. The following table gives their year one data:

Demand for the product is forecast to increase each year following a tringle distribution with a best case of 20% per year, worst cast of 5%, and most likely of 15%, i.e. 5/15/20%.

Market share is expected to grow uniformly between 5% and 12% per year.

The group opinion is that the price Charlie can charge can only increase slowly due to competition. The annual increase is normally distributed with a mean of $10.00 and a standard distribution of $2.50 ($10.00, $2.50)

R&D costs will decrease following a uniform distribution of 10 to 12% per year. Variable unit costs will increase following a triangular distribution of 5/7/9%. Overhead costs will increase following a normal distribution (10%,3%).

Marketing costs will increase each year at a rate that is normally distributed (10%, 5%).

Build a Crystal Ball model and run 3,000 simulation trials, find the five-year cumulative profit and explain the percentile report. Generate and explain a trend chart showing net profit by year.

What is the probability they will break even in year 2?

What it the probability the cumulative five-year profit will exceed $2,000,000? Include graphs for each year's profits and the trend chart.