What algorithm can solve a linear minimization problem with given constraints?

[specone]

Hi all,

does anyone know what type of problem this would be classified as, and what kind of algorithm I could use to get a solution?

minimize:
P=60w₁+30w₂+10w₃+100w₄

subject to:
P ≥ 50
0 < w_i ≤ 1

thanks very much

 

[mathman]

What are you trying to minimize? Without this, the question is incomplete. Defining what you want to minimize with these conditions is called linear programing.

 

[AlephZero]

It looks like a Linear Programming problem. The most straightforward solution algorithm is the Simplex Method.

 

[HallsofIvy]

The fundamental result in "linear programming" is that a minimum or maximum of a linear function, in a convex polyhedron, must occur at a vertex of the polhedron. Your condition, $0< w_i\le 1$, says that the "feasible region" is a n-dimensional rectangle and it is easy to calculate its $2^n$ vertices. However, the condition S> 50, on the target function will have to be applied after determining values. Also the fact that the faces $0= w_i$ are NOT in the feasible region can be a problem.