Solve the hotel example we investigated during the class $($Lecture $3,$ Slides $31-37)$ for high$-$fare customer demand following an exponential distribution.

A hotel with $250$ rooms

$-$ Low fare, $\backslash ($ F$\_\{$L$\}=\backslash$$ $125\backslash ),$ targeting leisure travelers

$-$ High fare, $\backslash ($ F$\_\{$H$\}=\backslash$$ $200\backslash ),$ targeting business travelers

$-$ Demand for low$-$fare rooms is abundant $($plentiful$),$ and commonly happens long before the date of stay

$-$ Demand is exponentially distributed with $\backslash (\backslash$boldsymbol$\{\backslash$mu$\}=\backslash$mathbf$\{62\}\backslash ).$

Answer the following questions:

$1.$ What is the high$-$fare protection level, $\backslash ($ Q$\_\{$H$\}\backslash )?$ What is the low$-$fare booking limit$,\backslash ($ b$\_\{$L$\}\backslash )?$

$2.$ Write down the expected revenue function $($do not solve it$!!!)$

You are free to solve either in excel or by hand using formulations. Submit only a single file $($preferably a pdf or word file$).$ If solved in excel, you can take a screenshot and separately show the cell formulations.