- Problems which seek to maximise (or minimise) a function subject to certain constraints are called optimisation problems.
- A Linear Programming Problem (L.P.P.) is the one that is concerned with finding the optimal value (maximum or minimum value) of a linear function of several variables (called objective function), subject to the conditions that the variables are non-negative and satisfy a set of linear inequalities (called constraints). The variables are sometimes called the decision variables.
For example: The following is an L.P.P.
Maximize Z = 10x + 12y
Subject to the following constraints:
5x + 3y ≤ 30 ... (1)
x + 2y ≥ 2 ... (2)
x ≥ 0, y ≥ 0 ... (3)
In this L.P.P, the objective function is Z = 10x + 12y
The inequalities (1), (2), and (3) are called constraints.
- The common regio…
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