Question 529297: okay so tomorrow i have a math test and two questions are over maximizing an objective function, and there wroth 20 points but the problem is that my teacher did not teach me how to do it. so i need your help because i have never even heard about this before.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! Not sure what your problem is, but I'll try.
You may have a function to maximize, like the profit for some business, that is hopefully a linear function of two variables, looking something like
 .
Maybe the function is the cost of something and you want to minimize it instead.
If your function is linear (meaning no exponents on your variables), the problem is simple, and read on.
You may have some constraints, like
 ,  and 
that you can figure out from the text of your problem.
You can draw x and y axes and plot the space that you have within those constraints.
In the case above, it would be a triangle limited by the lines
 and
You find the vertices of that space>
In the example above the vertices (corners) are (0,0), (0,20) and (20,0).
Find the value of your linear function (like the profit) at those corners of your space.
Look for the maximum (or minimum if you were minimzing).
The corner that gets it is where the maximum (or minimum) happens.
If two corners tie for the result, the line connecting them is where the maximum (or minimum) happens.
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