Alternate Method:
Instead of evaluating the objective function at all the extreme points; a graphical optimum solution can be
obtained which is explained below.
Consider the objective function
Z = 4x + 7y
Assign a convenient arbitrary value for Z say Z = 140, then
Z = 4x + 7y = 140
This is a straight line, which can be represented in the solution space as shown in figure 11.
Consider Z = 4x + 7y = 140. If x = 0, we get y = 20 and if y = 0, we get x = 35. These two points are connected by a
straight line representing Z = 140.
Thus Z = 140 is called an iso-profit line since for all points in the straight line, Z = 140. With this value we
have obtained the slope and hence shape of the straight line.
Next step is to draw straight lines parallel to 4x + 7y = 140.
This results in moving the objective line with various values in the solution space in a proper direction
(upwards in this example for maximization and downwards for minimization). In this process, the objective line may
cross a corner point indicating the maximum or minimum value.
Drawing parallel lines we see that a line passing through C (30, 30) gives the maximum value for Z and
value of Z* = 330.
Example
Minimize Z = 4x + 5y
Subject to x + y > 10
2x + 5y > 35
x, y > 0
Solution
STEP 1 Represent the constraints graphically
Consider x + y = 10
If x = 0, then y = 10
If y = 0, then x = 10
Consider 2x + 5y = 35
If x = 0, then y = 7
docsity.com
