(Solved by Humans)-A group of college students is planning a camping trip during the

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?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 0?1 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.