The following simulation modelling problem is quite difficult. If you successfully do this
problem, it will fulfill the “A” breadth requirement for problem set 3a.
A bus driver must carry a certain amount of change for passengers who do not have the
exact fare. If the driver cannot provide the correct change, the passenger is allowed to
ride free. The fare for the bus is 35 cents and previous experience has shown that
passengers will board the bus with the following money for the fare:
1 quarter + 1 dime
1 quarter + 2 nickels
3 dimes + 1 nickel
2 dimes + 3 nickels
2 quarters
4 dimes
1 dollar bill
1 five dollar bill
20%
10%
5%
3%
25%
7%
25%
5%
For security reasons, the bus company wants drivers to start with as little cash as is
reasonable to make the necessary change. Suppose a driver starts out with $10 in
change. As they pick up passengers, their change purse both grows and alters in
composition. Build a simulation model that allows you to choose different combinations
of nickels, dimes, quarters and 1 dollar bills (that add up to $10) that the bus driver will
start the day with. Simulate a typical day where 100 passengers board the bus. Does
the initial combination of coins affect the number of free rides that must be given? Can
you arrive at an optimal mixture of the initial cash?