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# Graphical solution - Objective function coefficient

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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.

https://brainmass.com/math/graphs-and-functions/graphical-solution-objective-function-coefficient-172747

#### 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

\$2.19