Introduction to Linear Programming

Many business decisions require making decisions to get the best possible return within a set of given constraints. For example, consider a farmer with access to both high grade and low grade fertilizer. The high grade material is more costly at $12/bag than the low grade which only costs $4/bag. The farmer can afford $60 worth of fertilizer per hectare. What possible combinations of bags could he choose? This page requires a Java capable browser.

Let x represent the number of bags of high grade fertilizer.

Let y represent the number of bags of low grade fertilizer.

We can write the different ways the farmer can spend his $60 as:

12x+4y=60

This is the equation of a line. If you haven't changed anything on the applet to the right, this is the line shown. (If you have changed something, pressing 'r' in the applet should reset it.) You can drag the red point along the line to see the different combinations of bags the farmer could buy. What whole number combinations of bags are possible?

Exercise 1.

Use the applet to find all of the non-negative whole-number combinations of x and y which satisfy the following linear equations. Drag the yellow dots to change values of a, b and c.

a) 5x+4y=24

b) 3x+5y=35

c) 4x+6y=54

Introduction to Linear Programming

Exercise 1.

Check your answers