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Problem 4 Melvin sells hotdogs in Macy's . The following graph shows the cumulative distribution function for the number of people who will demand...

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Problem 4Melvin sells hotdogs in Macy's . The following graph shows the cumulative distributionfunction for the number of people who will demand hotdogs from Melvin's store :`F ( x )0. 8 {0. 5 to^0. 2 7 -80180 250 300400Quantity ( x )Note : F ( 60) = 0 and F ( x ) > O for * = 60 .Melvin wants to determine how many hotdogs to stock . He sells hotdogs at $1. 02 each , andeach hotdog costs $0. 60. Operational costs are ignored .( 2 ) Melvin can liquidate the unsold hotdog material to sellers who run streethotdog stands in the evening . First 40 % of the hotdogs will be bought from him at$0. 30 , and the remaining 60 % will be bought from him at $0 . 10 by the street sellers .What is the critical fractile ? How many hotdogs should Melvin stock ?!C = 1. 02 - 0. 6 = 0 . 42Co = 0 . 6 - 0. 4 . 0. 3 - 0 . 6 . 0 . 1 = 0 . 42F ( Q * ) 2 0 . 5\Therefore we have Q* = 250( b ) One of Melvin's friends became an accountant and gives him a practical tipthat he can get 100% saving in his income tax report for the entire unsold hotdogs , if he*donates them to a nearby charity and keeps the receipts . Assuming his friend is telling*the truth , what is the minimum amount of hotdogs that Melvin should stock ?!Co = 0 , 50 F ( Q " ) = 1 . Therefore we have Q' = 400 .12
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