# 1. Consider the inventory example presented in Sec. 16.1 except that demand now has the following…

1. Consider the register model presented in Sec. 16.1 ate that call-for now has the following presumption distribution: P{D _ 0} _ _ 1 4_, P{D _ 2} _ _ 1 4_, P{D _ 1} _ _ 1 2_, P{D _ 3) _ 0. The enjoining management now is newfangled to enjoining impartial 2 cameras at the end of the week if none are in fund. As antecedently, no enjoin is placed if there are any cameras in fund. Assume that there is one camera in fund at the interval (the end of a week) the management is established. (a) Construct the (one-step) transition matrix. (b) Find the presumption distribution of the recite of this Markov compact n weeks after the new register management is established, for n _ 2, 5, 10. (c) Find the ij (the expected original paragraph interval from recite i to recite j) for all i and j. (d) Find the steady-state probabilities of the recite of this Markov compact. (e) Assuming that the store pays a storage absorb for each camera retaining on the rejection at the end of the week according to the part C(0) _ 0, C(1) _ $2, and C(2) _ $8, find the longrun expected medium storage absorb per week.