Step 2: Graph the Objective Functio

Step 2: Graph the Objective Function
The objective function can be graphed in a similar way to the constraints. The only difference is that the equation representing the objective function has no right-hand side value. If an RHV value is arbitrarily assigned, then the line of the objective function can be graphed by determining two points, as explained in the previous section. For easy calculations, a value of zero can be assigned to the objective function, which forces its line to pass through the origin of the Cartesian space.

When assigning a value of zero in the objective function, the equation becomes:
Z = 400x1 + 300x2 = 0
If x1 is equal to 0, then 300x2 is equal to 0, which leads to x2 also becoming 0, as such the point (0, 0). Another
point is needed to determine the straight line: If x2 = 4, then:
400x1 + 1,200 = 0, which leads to 400x1 = −1,200 and x1 = −3
So, the objective function must also go through point (−3, 4). The objective function line, connecting the points (0, 0) and (−3, 4), is shown in red in Figure 2-2.