# Graphical solution - Objective function coefficient

Use a graph to illustrate why a change in an objective function coefficient does not necessarily lead to a change in the optimal values of the decision variables, but a change in the right-hand sides of a binding constraint does lead to new values.

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#### Solution Preview

Use a graph to illustrate why a change in an objective function coefficient does not necessarily lead to a change in the optimal values of the decision variables, but a change in the right-hand sides of a binding constraint does lead to new values.

This condition can be explained by following example:

Objective function: Maximize Z= $400C + $100T

Subject to constraints:

8C+10T<= 80

2C +6T<=36

C<=6

C,T >= 0

CHANGE IN OBJECTIVE FUNCTION CO_EFFICIENT:

Following graph shows the graphical solution to above problem. The shaded region represents feasibility area for the problem. Optimal solution: C=6, T=3.2, Z=$2720

The shaded are shows the feasibility region and the pink line shows ...

#### Solution Summary

This solution provides details on why a change in an objective function coefficient does not necessarily lead to a change in the optimal values of the decision variables