Question 3 (15 points): A mountain climber is planning to go to hiking in Rocky mountain in the west of Canada. She is going to carry only one knapsack with herself. The maximum amount of weight that she can carry is 15 kg. She has the following list of items with different weights and importance levels. Items Weight (kg) Importance Item 1 5 4 Item 2 3 9 Item 3 7 4 Item 4 3 7 Item 5 9 2 3 6 Item 6 Item 7 Item 8 1 2 9 1 Part a) Write a mathematical programming model to help her choose the best combination of items such that the sum importance of carried items is maximized. (6 points) Part b) Items 5, 6, and 8 are useful only when they are carried together and totally useless if any of them is not colo How would you consider this information in your model? (2 points) Part c) The hiker knows that she has to choose exactly 2 items among items 2, 5, 7 and 8. How would you consider this information in your model? (2 points)