Youare supposedto be at your desk ready forworkat 9:00 AM.Youcannot belate or you will be fired, butitis fineif you arrive early. You figurethat eachminute you spend at work before 9 AM costs you 3 cents. You also know that there is a function that describes the amount of time it will take you to get to work that is:
Commute Time ¼ 15 minutes þ 0:1(Departure Time minus 8 AM)
þ 0:04(Departure Time minus 8 AM)
2 Departure Time minus 8 AM is measured in minutes. Your value of reductions in commuting time is 5 cents per minute.

a. What is your optimal departure time?

b. How much time do you spend commuting?

c. When do you arrive at work?

d. What happens if you decide that time spent at work before 9 AM costs you 3.1 cents per minute instead of 3 cents?