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.
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.
Joanne can carry not more than 3.6 kg of fruits home.
a) Write 3 inequalities to represent the information given above.
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.
These techniques are general purpose in that they take as input an LP and determine a solution without reference to any information concerning the origin of the LP or any special structure of the LP.
They are fast and reliable over a substantial range of problem sizes and applications.