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A sports club prepares for the celebration of a possible 20th championship of its football team in the junior league. The team has a large number of supporters, and the management thinks that they should be well-prepared for the possibility and plan the number of high-end sweat-shirts to procure from Italy. The unit cost of the shirt to the club is 32 TL, and it will sell for 130 TL. Any sweat-shirt not sold by the end of the short celebration period is purchased by regular stores to 20 TL/piece.
As a result of a number of detailed analyses the demand for sweat-shirts in case of a championship will have a normal distribution with a mean 150 (thousand) and a standard deviation of 30 (thousand) units.
a) Given that the ordering quantity is Q*, what is the expected number of sweat-shirts not sold?
Write the expression in terms of Q* and compute.
b) Given that the ordering quantity is Q*, what is the expected excess demand for sweat-shirts?
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