5. Consider the following inventory problem. A camera store stocks a Particular model camera that can be ordered weekly. Let D1, D2, . . represent the demand for this camera (the number of units that...

Extracted text: 5. Consider the following inventory problem. A camera store stocks a Particular model camera that can be ordered weekly. Let D1, D2, . . represent the demand for this camera (the number of units that would be sold if the inventory is not depleted) during the first week, second week, ..., respectively. It is assumed that the D; are independent and identically distributed random variables having a Poisson distribution with a mean of 1.5. Let Xo represent the number of cameras on hand at the outset, Xı the number of cameras on hand at the end of week 1, X2 the number of cameras on hand at the end of week 2, and so on. Assume that Xo = 3. On Saturday night the store places an order that is delivered in time for the next opening of the store on Monday. The store uses the following order policy: If there are no cameras in stock, the store orders 3 cameras. However, if there are any cameras in stock, no order is placed. Sales are lost when demand exceeds the inventory on hand. Thus, {Xt} for t = 0, 1, ... is a stochastic process of the form just described. The possible states of the process are the integers 0, 1, 2, 3, representing the possible number of cameras on hand at the end of the week. The random variables Xt are dependent and may be evaluated iteratively by the expression max{3 – Dt+1 , 0} max{X¢ – Dt+1 , 0} if X¢ > 1 if Xt = 0 X++1 = }{ for t=0,1,2,... 7 (a) evaluate the various transition probabilities (b) Obtain the transition matrix for the above problem.