You are in charge of selecting the number of buses to put in operation at each time period in a city. Each bus that you select can only start at the following times:

12:00am

4:00am

8:00am

12:00pm

4:00pm

8:00pm

Each bus that is put in operation will be in operation for 8 hours. So, as an example, if a bus starts at 4:00am, it will continue to be in operation until 12:00pm.

The number of buses that are required to be in operation varies during different times of the day, as follows:

12:00am - 4:00am: 20 buses

4:00am - 8:00am: 22 buses

8:00am - 12:00pm: 35 buses

12:00pm - 4:00pm: 25 buses

4:00pm - 8:00pm: 40 buses

8:00pm - 12:00am: 23 buses

Problem 4a

What is the minimum number of buses required to cover the demand?

Problem 4b

The cost to start a bus varies based on the time of day, as follows:

12:00am: $35

4:00am: $37

8:00am: $25

12:00pm: $26

4:00pm: $30

8:00pm: $36

What is the minimum cost way to cover the requirements?