Results:

After fulfilling all the variables and constraints in the Excel, We run the Excel solver tool and choose to create the answer reports and the sensitivity reports. The Answer Report, as we all knew that, it can provide basic information about the decision variables and constraints in the model. It also gives us a quick way to determine which constraints are binding and which constraints have slack. Our data illustrated in the Answer Report are shown here:

It can be seen that the final value which is the optimal objective function value is $1,522,130. (one million, five hundred and twenty two, and one hundred thirty)

And the optimal solution is shown in the table below:

As the result, the number of Swimming(X1), Body Combat(X4), and Spinning Bike(X5) courses reach the maximum limitation. The result does not surprise us at all and it goes just like what we thought at the beginning. Because these three are the most profitable courses. We should have them as many as possible as long as they are under the resources constraints.
The bottom table shows the status of the resources under the optimal solution.

In order to maximum the profit, we need to monitor the resources. Some of them indicating binding and zero slack which means that if we change the value of them, the optimal solution will have to change. It’s worth to mention that Demand is not used up in this optimal solution. The information tells us that the Sporting Center still have rooms to be improved to attract more customers . For example, the Sporting Center can hire more Teaching Assistants or increase their electricity expense budget.

Except the Answer Report, we have run the Sensitivity Report which can explain the data accuracy and robustness.

This report tells us that the optimal solution is pretty robustness. Because the range we can change the profit margin