A group of students is planning a camping trip. One student, An, in this group, has identifiled 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 iem on a scale of 1 to 100, with 100 being the most beneficial. The item weights in pounds and their utility values 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 20 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.
Formulate this as a LP problem to maximize the total utility of items carried.