After you write the problem, you should solve it via the QM software, considering the requirements below:

You should first write the business problem you figured up (related to the business subfield requested) by explaining what the problem is. Then, you should define what the objective is, what you want to learn for optimization, and what your limitations are. Please be sure you are explaining these clearly and in detail.

The number of decision variables should be 8, 9, or 10, and the number of constraints should be 10, 11, or 12 in the model. (Therefore, please write your business problem accordingly).

You should show me in your report in a separate section that what you have written (figured up) in your scenario corresponds to which equation (objective function and constraints) in your mathematical model. For example, clearly, you should clearly show me the third constraint coming from which sentence in your scenario.

By using QM software, you should show the optimal solution (i.e., the optimal values of decision variables and objective function). Please share the screenshots in your report (please elegantly).

You should write the results of the sensitivity analysis and summarize the important findings in your sensitivity analysis. Please share the screenshots in your report.

2. Your second task is to formulate a mixed integer linear programming model by adding one binary (0- 1 integer) variable (not more than one!!!) to the business problem you wrote in the first task. Then, please solve this problem via the QM software considering the requirements below:

Write how you modified the story of your business problem after adding the binary variable.

Please also define your binary (0-1 integer) variable and then show how its addition to the model requires changes in the math equations of objective function and constraints.

By using QM software, you should show the optimal solution (i.e., the optimal values of decision variables and objective function). Please share the screenshots in your report.

There is no need to make the sensitivity analysis again.

Additional Important Information

It is your responsibility to design a model that gives a feasible and bounded solution. I will not consider models that provide infeasible and unbounded solutions because they imply you are making logical fallacies while modelling the problem.

Definition of business problems in accordance with homework requirements. (20 pts) o Proper mathematical model in aligned with the defined problems. (20 pts) o Highlighting clearly which math equation represents which part of the problem. (15 pts) o The outputs of problem solution and sensitivity analysis. (15 pts) o The detailed interpretation of sensitivity analysis results. (15 pts) o The quality of the report in terms of language, structure, figures, clarity and etc. (15 pts)