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Cost: 100,99

Read Speed: 545,550

Write Speed: 525,520

Warranty: 3,4

This means that there are 2 products that cost $100$ and $99$. Their read speed is 545 MB/s and 550 MB/s. Their write speed is 525 MB/s and 520 MB/s respectively. Their warranty is 3 years and 4 years respectively. Now, I need to choose the best product between the two.

What technique do I use to solve this? This is just a dummy problem because I want to learn the technique to solve these kinds of problems for bigger scales like 50 different products.

I've been told that under given circumstances this problem isn't solvable. Say, I put constraints like:

write speed>500

read speed>520

warrranty>3

cost<$99.99

Is this solvable now? If yes, how? I've been getting told that this could be solved by linear programming. I've a background in engineering mathematics so if you can provide some insights, hopefully, I can solve this problem.

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  • $\begingroup$ What's the objective? What are the constraints? $\endgroup$
    – fontanf
    Sep 15, 2022 at 10:12

2 Answers 2

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If you are just choosing between two or more products, it has nothing to do with linear programming. You are looking for a utility function to rank the products. Typically, this presumes that (a) you have multiple decision makers and (b) each is capable of looking at a pair of products and deciding which one they prefer. You might want to look at the Wikipedia entries for multi-attribute utility and maybe the analytic hierarchy process. In the latter, you ask the decision maker(s) questions like "which is more important, cost or warranty, and by how much?".

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If someone told you that linear programming could be applied to this problem, it could be that they were thinking of Data Envelopment Analysis (DEA), - see Wikipedia. DEA assumes a linear utility, i.e., you choose a weight for each feature such as read speed, cost, etc. For a given set of weights, the preferred device is the one that maximizes the weighted sum. DEA answers the questions:

For each device j:
Is there a set of weights that makes j the preferred device, or if the device is dominated, is there no set of weights that makes device j preferred.

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