A scalper is considering buying tickets for a particular game. The price of the

Question

A scalper is considering buying tickets for a particular game. The
price of the tickets is $75, and the scalper will sell them at $150. However, if she can't
sell them at $150, she won't sell them at all. Given that the demand for tickets is
a binomial random variable with parameters n = 10 and p = 1=2, how many tickets
should she buy in order to maximize her expected pro t?

DO NOT use this: (n+1)p rule, that's not how we should find the answer.

In your answer you should use the values of 150 and 75.

I tried brute forcing it but im not sure if im doing it the right way,

Explanation / Answer

    expected profit is 282.7148 when she buys 5 tickets.

M = number of tickets she buys

M can vary from 0 to 10 .

X - demand

Profit (Xi) = 75 * min (Xi, M) -75 (n - min(Xi,M))   { check yourself

for example if n = 3 , and she purchase 5 ticket

then profit = 75 * 3 -2*75 = 75 . {check in table above

expected profit = sum p(Xi) * P(Xi)    

you can take all values of M from 0 to 10 , or use solver to maximize expected profit

we get M = 5 whose calculations are shown above

Please rate

n X p(X) 5 1 0 0.000976563 -375 -0.36621 10 1 0.009765625 -225 -2.19727 45 2 0.043945313 -75 -3.2959 120 3 0.1171875 75 8.789063 210 4 0.205078125 225 46.14258 252 5 0.24609375 375 92.28516 210 6 0.205078125 375 76.9043 120 7 0.1171875 375 43.94531 45 8 0.043945313 375 16.47949 10 9 0.009765625 375 3.662109 1 10 0.000976563 375 0.366211 sum 282.7148

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