I have formulated a linear optimization model and solve it using the Excel Solver. How can I illustrate the slacks vs usage?

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    $\begingroup$ Hello, and welcome to OR.SE. Your question is quite broad, and it will be difficult for us to provide a helpful answer. Please edit your question to indicate what, precisely, you are asking about. We can't (or won't) usually answer questions that just say "did I do this homework problem correctly?" But we're happy to try to answer questions that explain what you did, where you got stuck, and what aspect you need help with. $\endgroup$ – LarrySnyder610 Mar 11 at 20:36
  • $\begingroup$ @LarrySnyder610, thank you for your feedback. I edited my question :) $\endgroup$ – user3176 Mar 11 at 20:56
  • $\begingroup$ I still don't really understand what you are asking. You know the usage (I assume you just mean the values of the decision variables) and you know the slacks, so can't you just plot them? Or do you mean something more specific when you say "graphically illustrate"? $\endgroup$ – LarrySnyder610 Mar 12 at 1:31

I'm not sure I understand your question as well but, let me describe an example using excel. In the following tiny instance, the model has two variables and four constraints.

\begin{alignat}{5} \max \quad & z = & 3x_1 & + & 2 x_2 & & & &&\\ \mbox{s.t.} \quad & & x_1 & + & x_2 & \leq 9 && \tag{constraint 1}\\ & & 3x_1 & + & x_2 & \leq 18 && \tag{constraint 2}\\ & & x_1 &&& \leq 7 && \tag{constraint 3}\\ &&&& x_2 & \leq 6 && \tag{constraint 4}\\ && x_1 , x_2 \geq 0 \end{alignat}

When the model is solved, the objective function value is 22.5, and the decision variables have the value, equal to 4.5. Also, the dual and slack values will be found by the solver.

enter image description here

Based on the results, you can illustrate the data using excel chart. (E.g. the usage chart to depict the value of the decision variables or comparing RHS vales and whose slack.). However, if you are interested to use "Sensitivity Analysis", you can go ahead. I hope it would be helpful.

enter image description here

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