Optimizing Production with Linear Programming in Economics: A Math Question

[Izekid]

This is a economic math question see if you can help me out here.

I've got 3 variables A,B and C and I shall get the production to be optimal I have there variables

This is the formula = Z = 800A+ 550B +400C
Under these condition it shall work

14A+10B+8C=<4500
12A+7C=<1000
12A+18B+10C=<480
A,B,C>0

With these numbers I shall get a number for each variable that should be the best production way.
It's called in mathematics, Linear Programming

http://www-unix.mcs.anl.gov/otc/Guide/faq/linear-programming-faq.html

I have tested many thing please help me if you can

 

[HallsofIvy]

First convert the inequalities into equations:

14A+ 10B+ 8C= 4500
12A+ 7C = 1000
12A+ 18B+ 10C= 480

Those equations define planes that form the boundary of the "feasible area". Solve for values of A, B, C to get the vertices of that area.
The evaluate Z at each of those vertices. The optimal value will be at one of the vertices.