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I am little new to this platform, but i think you guys can help me. I have a question that I cannot solve.

Here's the problem.

You can only carry $25$kg on your backpack. only choose one thing from each set. find the most survival point using mathematical programming.

I tried to use linear programming but my objective function was incorrect.

I tried to tag them as x1,x2,x3 or x1-1 , x1-2 x1-3 but I couldnt find how to model this question. I guess its dynamic modelling and I dont know that one.

Sorry for my bad English :) Thanks everyone for your help!

thank you for your help. you can find the graphic in picture. actually I dont know which method to use. please help.

Should I solve it with matrix?

Esra Akbulut
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  • my grapic isnt here how can i add? I need help :( – Esra Akbulut Nov 11 '18 at 14:57
  • Your picture is there ... I see you can carry a 12 kg turkey for 25 survival points – Bram28 Nov 11 '18 at 15:00
  • hi thank you but, I have to choose one, from each,one turkey one water one shelter and one defense. and must have the most possible survival points, but I can carry only 25 kg in my backpack. and I have to solve it with mathematical programming. :) – Esra Akbulut Nov 11 '18 at 15:03
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    Welcome to MSE. You'll get a lot more help, and fewer votes to close, if you show that you have made a real effort to solve the problem yourself. What are your thoughts? What have you tried? How far did you get? Where are you stuck? This question is likely to be closed if you don't add more context. Please respond by editing the question body. Many people browsing questions will vote to close with reading the comments. – saulspatz Nov 11 '18 at 15:06
  • It's not really linear, is it ... – Bram28 Nov 11 '18 at 15:08
  • Hi again dear Saulspatz :) I really really tried so hard, at my best but I dont know how to overcome this. Actulayy I dont know how to write this down for modelling I am stuck really bad :) – Esra Akbulut Nov 11 '18 at 15:28
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    This might help: https://en.wikipedia.org/wiki/Knapsack_problem – Ethan Bolker Nov 11 '18 at 15:40
  • Have you seen 0-1 ILP? One way is to use three 0-1 variables for each category (e.g, food), imposing the constraint that they are mutually exclusive: $\sum_{1 \leq j \leq 3} x_{ij} \leq 1$. – Fabio Somenzi Nov 11 '18 at 16:09
  • It helps if you tell us what you know about. As Fabio has pointed out, the problem can be modeled as an integer linear programming problem, with $0-1$ variables. Are you familiar with that? If not, tell us what you are studying, so we can try to give a suitable answer. – saulspatz Nov 11 '18 at 21:16

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This is such a tiny problem that it can be solved using bare common sense. Taking the largest object of each set gives $90$ survival points, but $10$ kg overweight. In order to cut back significantly on the weight we should stay with the largest defense object. Going back one step on each of food, water, and shelter costs $15$ survival points and saves $11$ kg. Going back two steps on one of these also costs $15$ survival points, but is insufficient concerning weight. We therefore should choose the first described option, resulting in 75 survival points.

Christian Blatter
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