Queen Elizabeth employs six workers in her palace who come to work in the morning

and go home at night. The workers must enter the palace by one of two passages--the

Long Passage or the Narrow Passage. The Long Passage is indeed long, but it is so wide

that it always takes 44 minutes for a worker to enter through this passage, no matter how

many workers use it each morning. The Narrow Passage is much shorter, but is so

narrow that passage congestion is a problem when more than one worker at a time uses it

to enter the palace. For the Narrow Passage, the number of minutes each worker will

need to enter the palace is given by the formula: M = 34 +2W (where M is the number of

minutes it takes each worker to enter the palace, and W is the number of workers entering

through the Narrow Passage each morning).

a. Assume that the entrances to the two passages are right next to each

other, and that when workers approach the entrances to the passages in the

morning, they can tell how many workers have already entered a passage.

Further assume that each worker will choose to enter through whichever

passage offers him/her the lowest expected commuting time into the

palace. In this situation, how many of the six workers will be entering the

palace through the Narrow Passage each morning?

b. If the Queen wishes to minimize the sum of the time spent by the six

workers entering the palace each morning (and can only affect this sum by

instructing workers as to which passage to take) what should be her

guiding principle in assigning workers to passages?

c. Why won't the workers, acting individually, be guided by the same

principle as the Queen?

****** I'm confused on part b. how would she advise them differently? as part c suggests.