Jtrix Inc. offers high end, specialized testing services to contract manufacturers (CM) of semiconductor equipment. Its weekly testing capacity is 125 hours, and it is sold in 1-hour blocks for $140/hour. The internal operating cost of its testing equipment is $100/hour. Because of demand uncertainty induced by the recession, in the recent past, CMs have often cancelled their orders for testing at the last moment. Jtrix estimates that the number of cancelled hours can be approximated by a Poisson distribution with a mean of 14 hours (see the table below). Jtrix does charge a cancelation penalty of $40 per canceled hour (that is, if a CM books an hour but then cancels, they still pay Jtrix $40). If Jtrix ends up with unused capacity due to cancellations, it is unable to sell that capacity to another customer, but it also doesn't incur the operating cost of $100/hour (that is, the $100 is incurred only when operating). If it's available capacity is insufficient to meet the booked demand, Jtrix has the option to cannibalize testing time from its sister facility. However, doing so is expensive for Jtrix, and increases its operating cost to $150/hour.
a. Suppose Jtrix decides to overbook by 10 hours each week, i.e., it sells exactly 135 hours of testing capacity each week. On average, how many hours of unused testing capacity will it have in a given week?
b. Suppose Jtrix decides to overbook its capacity. How many hours should Jtrix sell to CMs?