2.03 Finding Maximum and Minimum Values

Introduction

Linear programming is a method for finding minimum or maximum value of a function, given a set of constraints, or limits, for the variables in the function.

Here is a simple example. The function you want to maximize is P = −2x + 3y.

The constraints on x and y are:
1 ≤ x ≤ 3
0 ≤ y ≤ 2

You must find the values of x and y, within the given constraints, that give the maximum value for P. To do this, choose a value for each variable and plug it in to the function P. Keep trying until you find the maximum value for P.

For example, suppose you choose x = 2 and y = 1. When you plug it in to P, we get P = −2(2) +3(1) = −1.

So, P = −1 (the value of P is −1) when x = 2 and y = 1. Now try other values for x and y until you get the maximum value for P. Then complete the following:

The maximum value for P occurs when x = ______ and y = _____. Answer

 

The maximum value for P occurs when x = 1 and y = 2, so the maximum value of P is ______. Answer