The Berlin Airlift

A cost function usually specifies a quantity to be minimized. In the present case, you're trying to maximize the cargo capacity. A more general term for a function to be optimized (minimized or maximized) is "objective function". If you want to use an optimization algorithm or package that expects a cost function to be minimized, you can let it minimize the negative of the function to be maximized. In the present case, the cargo capacity to be maximized is $30000x+20000y$, so you could use $-30000x-20000y$, or equivalently $-3x-2y$ as a cost function.

Regarding planes and flights, the problem statement is a bit vague in that respect: It constrains the "total weekly costs", but it doesn't specify the time period over which "no more than 44 planes could be used". From the inequalities you cite, it seems that "weekly" is irrelevant and all the restrictions given are intended to apply to some common time period; otherwise the inequalities shouldn't all be using the same variables $x$ and $y$ without any time factors.


The problem has already been analyzed by @joriki. You can get a numerical solution by trying an online Simplex solver. Just google for it. I tried the first one that I found: Simplex Method Tool and got for the maximal capacity c:

enter image description here

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Optimization

Linear Programming

Operations Research

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