Optimizing Production with Linear Programming in Economics: A Math Question

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The discussion focuses on optimizing production using linear programming with three variables: A, B, and C. The objective function is Z = 800A + 550B + 400C, subject to specific constraints represented by inequalities. The user seeks assistance in converting these inequalities into equations to define the feasible region for the variables. The key steps involve solving for the vertices of this feasible area and evaluating Z at each vertex to find the optimal production values. The optimal solution will be located at one of these vertices, maximizing the objective function.
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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 forumla = 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
 
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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.
 

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