Answer to Question #206352 in Math for Tshimo

Question

The manager of the industrial plant is planning to buy a new machine of either type A or type B. For each day’s operation the number of repairs X that machine A requires is a Poisson random variable with mean 0,10t, where t denotes the time (in hours) of daily operation. The number of daily repairs Y for machine B is Poisson distributed with mean 0,12t. The daily cost of operating A is C_A(t) = 10t  +  30X²  and for B it is C_B(t)  =  8t  +  30Y². Assume that the repairs take negligible time and each night the machines are to be cleaned, so they operate like new machines at the start of each day. Which machine minimizes the expected daily cost if a day consists of ten hours? Show

Answer 1

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