show calculations used to get each column table answerQuestion $1($Managing Fixed Capacity $-$ Dual Pricing$)$

The Curtis M Philips Center for the Performing Arts at UF is staging "Dear Evan

Hansen" on Monday, November $4,2024$ at $7$:$30$ pm$.$ With a fixed capacity of $1700$ seats

in the proscenium hall, the focus is on generating the maximum revenue $($profit$)$ for the

show.

Based on historical data, the Center manager knows that if all seats are offered at a "low"

price of $$25,$ occupancy will be $100\%($or all $1700$ seats will be sold$)$ and thus, revenue

obtained will be $(1700*25)=$$$42,500.$ Through a dual pricing strategy, the Center

manager is interesting in generating more revenue. Three dual pricing schemes under

consideration are:

Low price $p_1=$$$25$ and a High Price $p_2=$$$75.$ The demand for seats at the high

price of $$75$ is uncertain and normally distributed with a mean $=500$ and

standard deviation $=100.$

Low price $p{l}_L=$$$25$ and a High Price $p_2=$$$90.$ The demand for seats at the high

price of $$90$ is uncertain and normally distributed with a mean $=625$ and

standard deviation $=125.$

Low price $p_1=$$$25$ and a High Price $p_2=$$$105.$ The demand for seats at the high

price of $$105$ is uncertain and normally distributed with a mean $=750$ and

standard deviation $=150.$

You are required to:

Analyze the three dual pricing options and present your results in the following table.

Do these results support the following statement $"$By pricing all seats for sale at the

low price of $pL=$$$25($and thereby maximizing capacity utilization$),$ the Philips Center

can always generate the highest expected revenue?" Please provide analytics to support

your answer.