Problem$1$: Tulane Musical: We are planning to open a brand new play at the Saenger Theatre, New

Orleans, Tulane Musical! We estimate that development cost will be $$2\mathrm{.}5$ million for the show. There

are five shows per week. We have three shows on Saturday nights and two shows on Sunday nights.

The fixed cost of opening the theatre each night is $$2000($independent of number of shows in that day$).$

We project that the show will run for one year $($i$.$e$.52$ weeks$).$ Tickets sell for $$40.$ We also earn an

average of $$2\mathrm{.}5$ profit per ticket holder from concession stand, a place where customers can purchase

snacks or food. The theatre capacity is $1100$ seats, and we expect $80\%$ of the seats to be full.

a$)$ Set up a spreadsheet model for the inputs and output. Define range names for each input and

output. Paste a list of range names in your spreadsheet. Define your formula to obtain the

expected profit value$1.$ By using the formula in part a$),$ answer the following questions$($Don$$t

apply cumulatively$)2$:

b$)$ How many weeks will the play have to run for us to break even?

c$)$ What percentage of the seats should be filled for us to break even $($make sure you type $52$ in your

number of weeks cell to recover initial problem setting$)?$

d$)$ Set up a one$-$way data table to determine how an increase in the percentage of seats filled affects

the profit. Perform sensitivity analysis by changing percentage seats full from $60\%$ to $100\%$ with

$5\%$ increments $($make sure you have $52$ in your number of weeks cell and $80\%$ in percent seats

filled cell to recover initial problem setting$).$

e$)$ Set up a two$-$way data table to determine how a joint change in the ticket price $($from $$25$ to $$65$

with $5$ increments in the column$)$ and the number of weeks the play runs $($from $35$ to $75$ weeks

with $5$ increments in the row$)$ influence the profit