## Based on expected profit and expected percentage of unsold pretzels, how many pretzels should be ordered?

Question on Spreadsheet modeling and decision analysis:-

K’s brewery is sponsoring sports games and putting up “beer gardens”, selling drinks and snacks. For the first such event, the manager of the beer garden needs to determine how many pretzels to order. The local bakery offers a contract for 120, 150 or 180 pretzels, at a cost of Euro 0.40 each. The sales price is Euro 1.50. Any unsold pretzel is given to a charity.

If the game is interesting, the manager thinks that fewer people will come to the beer garden. In this case, demand is expected to be normally distributed, with a mean of 140 and a standard deviation of 20. However, if the game is boring, more people will come, with normally distributed demand (mean 190 and standard deviation 15). Based on the profile of the teams playing in the event, the manager thinks that there is a 40% chance that the game will end up being boring. Based on expected profit and expected percentage of unsold pretzels, how many pretzels should be ordered?