TV Advertising $(20$ points$)$

A TV Station has $20$ thirty$-$second advertising slots during their regularly scheduled

programming each evening. The station is now selling advertising for the first few days in

November. It could sell some or all the slots immediately for $$5000$ each. Whatever slots

that it doesn$$t see immediately, the station manager knows that she may be able to sell

them for a price at $$8,000$ each to political candidates $($since November $7$th is an election

day$).$ From prior years, she estimates that the demand for these political slots corresponds

to the following probability distribution:

Demand $8910111213141516171819$

Probability $0\mathrm{.}020\mathrm{.}040\mathrm{.}130\mathrm{.}140\mathrm{.}180\mathrm{.}190\mathrm{.}110\mathrm{.}040\mathrm{.}060\mathrm{.}040\mathrm{.}030\mathrm{.}02$

Slots not sold to political candidates can be readily sold at the last minute to local

advertisers at a price of $$1500.$

a$)$ How much revenue will the station receive if the station manager sells all the advertising

slots in advance? $($Handwrite answer. $5$ points$)$

b$)$ Construct a Simulation Modeling Template for estimating the revenue that the station will

receive if the station manager sells $10$ slots in advance. Do a manual simulation of the

revenue for $10$ trials using random numbers:

$0\mathrm{.}9642$

$0\mathrm{.}34413$

$0\mathrm{.}20232$

$0\mathrm{.}94271$

$0\mathrm{.}05192$

$0\mathrm{.}20501$

$0\mathrm{.}17359$

$0\mathrm{.}09059$

$0\mathrm{.}63029$

$0\mathrm{.}72947$

Please specify your Process Generator$($s$).$ Based on your $10$ trials, give an approximation of

the Risk Profile. What is the expected revenue over your $10$ trials? Based on your $10$ trials

which of the two possibilities, selling $10$ or $20$ in advance, do you recommend? Why?

$($Handwrite answer. $5$ points$)$

c$)$ Translate your Modeling Template in part $($b$)$ to EXCEL and simulate using EXCEL for $1000$

trials. What is the expected revenue? $($Submit via Blackboard. $5$ points$)$

d$)$ What gives the higher expected revenue $-$ selling $10$ in advance or selling $20$ in advance?

What is the probability that selling $20$ in advance will give a higher revenue than selling $10?$

What is the approximate Risk Profile of selling $10$ in advance using the bin range of

$$115,000,$ $$120,000,...,$ $$130,000?$