5. Linear Programming

1. optimization: 

We have a (single) objective (e.g., maximizing profit or minimizing cost).

We want to find optimal resource allocation using mathematical modeling.

We have supply (resource) and/or demand limitations.

2. Terminologies: 

Decision variables x1, x2,…, xn. We get to choose the values of these

Constraints express supply/demand limitations

f(x1, x2,…, xn) ≤ b

f(x1, x2,…, xn) ≥ b

f(x1, x2,…, xn) ＝ b

Objective function expresses the quality of an outcome

max/min g(x1, x2,…, xn)

If a constraint satisfies an equality, it is called binding (,tight, or zero slack).

If a constraint is not binding and LHS is greater than RHS, the difference is called surplus.

If a constraint is not binding and LHS is less than RHS, the difference is called slack.

3.