Question

Four friends (Amy, Brian, Camila, and Dinesh) are standing on the east bank of the Mississippi river and

wish to cross to the west bank using a canoe. From previous experience, Amy knows that she can row

(one-way) across the river in 5 minutes. She also knows that rowing back would take her 4 minutes more

(because of fatigue). More generally, the time Amy needs to cross the river on her

k

th

bank-to-bank trip

is adequately represented by the function 1 + 4

k

. Similarly, the time it takes Brian, Camila, and Dinesh

to row across the river on their

k

th

trip is correctly captured by the functions 3 + 3

k

, 7 +

k

, and 6 + 2

k

.

The canoe can hold at most two people at a time. If two people are in the canoe, both people are

rowing but the slower person dictates the crossing time. The objective is for all four friends to be on the

west bank of the Mississippi river in the shortest time possible.

1. Identify at least two feasible plans for crossing the river (remember that the canoe is the only mode

of transportation and it cannot be shuttled empty.)

2. Define the criterion for evaluating which alternative is best.

3. Use common sense to determine the smallest time needed for moving all four friends to the west

bank. Give an intuitive argument for why the solution you propose is “optimal”.

Answer 1

Amy    Brian   Camila Dinesh

1+4k 3+3k 7+k 6+2k

1st time up  5 6   8 8 k=1

down 9 9 9 8 k=2

2nd time up 13 12 10 12 k=3

down 17 15 11 14

Shortest time combination:

First time amy & brian goes time =6

brian return time = 9 (as amy's 2nd up & down time is high)

camelia & dinesh goes time = 8

camelia return time =9 ( as dinesh 2nd up & down time is high )

then brian & camelia goes time = 12 so total 6+9 +8 + 9 +12 =44 (Ans)