Question

2. (20 P.) Suppose that you are planning a picnic. You've constructed a list of items you would like to carry with you on the picnic. Each item has a weight associated with it and your knapsack is limited to carrying no more than 10 pounds. You have also come up with a to 5 rating for each item, which indicates how strongly you want to include the particular item in the picnic. This information is listed in the table below: Item Weicht (lb) 2 4 Weight (lb) Rating 3 (a) [8 P.) Formulate an optimization model to determine the combination of items that maximize your total ratings (b) (4 P.) select a constraint if either item A or item B but not both should be selected. A) XA + X8 21 B)*4 + x 51 C)XA2 Xs D) XA SX E) None of the above (c) (4 P.) select a constraint if item B shouldn't be selected if item A is selected, A) XA + X8 21 B) XA + Xe =1 C) XA2 X D) XA SX E) None of the above (d) (4 P.) select a constraint if at least 2 items must be selected. A) *x + x + x + x + x 2 2 B) x + x + x + x + x 52 C) XA + x + x + x + x 23 D) x + x + x + xy + x 53 E) None of the above

Answer 1

Anwen: Xi =0 9701 for ith item. where x; :o =) i it not relected X;=12 i is relected (a) Total Rating -axt XB 43xc tuxo +5XE Total weight = 2x^ + dpt 3 të turp t67€. Maximize = 2XA TXB t3 tc tu xp 7516 constraint a aratat 3 dct4d0 +62€ 210 di = {0,1} (b) porrible value for this case JA=0 23-0 and RAZO - sp=1 and AA1, AB=0 i alat&B SI A option B is correct JA= 1, Xp=0 12 = 1 +A=0 and JACO RB=0 XA EKBS I is dat die 31 :

(d) If at least 2 items is relected. Sat & B+ oct AD TRE EL option B i correct.