In these lessons, we will learn about linear programming and how to use linear programming to solve word problems.
Many problems in real life are concerned with obtaining the best result within given constraints.
While it may not be obvious that integer programming is a much harder problem than linear programming, it is both in theory and in practice.
The most widely used general-purpose techniques for solving IPs use the solutions to a series of LPs to manage the search for integer solutions and to prove optimality.
These methods derive from techniques for nonlinear programming that were developed and popularized in the 1960s by Anthony Fiacco and Garth Mc Cormick.
Their application to linear programming dates back to Narendra Karmarkar's innovative analysis in 1984. Due to advances in solution techniques and in computing power over the past two decades, linear programming problems with tens or hundreds of thousands of continuous variables are routinely solved.
An optimal solution is a feasible solution that has the smallest value of the objective function for a minimization problem.
An LP may have one, more than one or no optimal solutions.
Choose the scales so that the feasible region is shown fully within the grid.
(if necessary, draft it out on a graph paper first.) Shade out all the unwanted regions and label the required region It also possible to test the vertices of the feasible region to find the minimum or maximum values, instead of using the linear objective function.