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, Mae Jones, 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

Mae would like to maximize the utility to the items to be carried to the campsite, but 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. Mae has also decided that she will only take item number 5 if she also takes item number 3.

Formulate a programming model and solve using Excel. Determine the following:

a. In optimal solution, which items should Mae carry to the campsite?

I. Items 1, 2 IV. Items 5, 6, 7 VII. II & IV

II. Items 1, 3 V. Items 4, 5, 6 VIII. III & V

III. Items 2, 3 VI. I & V IX. I & IV

b. What's the total weight of the optimal selected items in pounds

c. Value of the objective cell?