A group of college students is planning a camping

trip during the upcoming break. The group must

hike several miles through the woods to get to the

campsite, and anything that is needed on this trip

must be packed in a knapsack and carried to the

campsite. One particular student, Tina Shawl, has

identified eight items that she would like to take on

the trip, but the combined weight is too great to take

all of them. She has decided to rate the utility of

each item on a scale of 1 to 100, with 100 being the

most beneficial. The item weights in pounds and

their utility values are given below.

ITEM 1 2 3 4 5 6 7 8

WEIGHT 8 1 7 6 3 12 5 14

UTILITY 80 20 50 55 50 75 30 70

Recognizing that the hike to the campsite is a long

one, a limit of 35 pounds has been set as the maximum

total weight of the items to be carried.

(a) Formulate this as a 01 programming problem to

maximize the total utility of the items carried.

(b) Suppose item number 3 is an extra battery pack,

which may be used with several of the other

items. Tina has decided that she will only take

item number 5, a CD player, if she also takes item

number 3. On the other hand, if she takes item

number 3, she may or may not take item number

5. Modify this problem to reflect this and solve

the new problem.