Question

How do I use linear programming to find maximum and minimum values?

Answer 1

Hint: Linear programming (LP) or Linear Optimisation may be defined as the problem of maximizing or minimizing a linear function which is subjected to linear constraints. The constraints may be equalities or inequalities. The main objective of linear programming is to maximize or minimize the numerical value. It consists of linear functions which are subjected to the constraints in the form of linear equations or in the form of inequalities.

Complete step by step solution:
In general, a linear programming graph will give you a polygon which contains all the possible combinations of the quantities involved.
The maximum and minimum values are found at the vertices, or if the vertices are not on whole numbers, then at the points inside the polygon which are closest to the vertices. If a linear programming problem can be optimized, an optimal value will occur at one of the vertices of the region representing the set of feasible solutions.
The maximum and minimum values are found at the vertices.
To solve a linear programming, we have the following:
Graph the region corresponding to the solution of the system of constraints.
Find the coordinates of the vertices of the region formed.
Evaluate the objective function at each vertex to determine which x and y values, if any, maximize or minimize the function.

Note: Some of the assumption taken while working with linear programming are: The number of constraints should be expressed in the quantitative terms, the relationship between the constraints and the objective function should be linear and the linear function (i.e., objective function) is to be optimised.