Optimal Outputs for Variable Inputs

[ThreeMarks]

I'd like to write a computer program that is capable of finding a set of outputs from varying properties of set of inputs.

So, for example, there are 10 possible inputs. Each input has, say, three shared properties and each of the inputs has verying values for those properties. E.g. we have a selection of 10 cars. Each car has a speed, comfort (assuming this can be measured) and cost and every individual car has it's own numerical quantities for these.

In this example, I would like to select three cars from these 10 so that cost is kept to a minimum, and that the average speed of the cars has a desirable fixed value (roughly) and the same for comfort.

Using math. how would you go about finding the best three cars. Or, more generally, an optimal set of outputs based on various inputs with certain desirable 'factors'. I don't need you to present the entire solution, but some ideas as to how I could go about doing so. Say, point me to some documents that explain this kind of situation.

Thanks.
ThreeMarks.

 

[Stephen Tashi]

This isn't the type of problem where you can express the answer as a formula (unless there is some systematic formula for the set of inputs). You can use "math" in the sense of computer algorithms to solve this problem. However, you need a more precise definition of what you want the computer program to do. For example, suppose the (Speed,Comfort,Cost) vector for one car is (0.90, 0.95, 0.83) and for another car it is (0.95, 0.90,0.83). Which car are you going to say is better?

It might help to have the computer program sort the list of cars according to a sort order - for example, one that emphasizes cost first, speed second and comfort third.