# How to find the product with best specs at least price?

Cost: 100,99

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

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.

• What's the objective? What are the constraints? Sep 15, 2022 at 10:12

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?".

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.