Problem #$4$: Orange Computers Inc. produces two models of laptops, A and B$.$ The central processing unit $($CPU$)$ in A is different from that in B$.$ Orange Computers orders the two types of CPUs every day from the same vendor following a base$-$stock policy. The daily demand for each of the two laptops follows a normal distribution with a mean of $100$ units and a standard deviation of $30$ units. The holding cost rate and backorder cost rate for the

CPU used in A are h $=$ $$0\mathrm{.}2$ per day per unit and b $=$ $$0\mathrm{.}8$ per day per unit, respectively. The CPU vendor has a leadtime of five days for both types of CPUs. Assume that there is always sufficient stock of all the other components used in a laptop.

Part A: What is the optimal target service level for laptop A based on these holding and backorder costs? Since each laptop has one CPU, the service level for laptop A and its CPU is the same. If your answer is not an integer, provide at least three decimal places, e$.$g$.,7\mathrm{.}500.$

Part B: What is the optimal base$-$stock level for the CPU used in A$?$ If your answer is not an integer, provide at least three decimal places, e$.$g$.,7\mathrm{.}500.$

Part C: Consider the CPU used in A alone. How does the average on$-$order $($pipeline$)$ inventory change if the leadtime for this CPU increases?

a$.$ Remains the same

b$.$ Increases

c$.$ Decreases

d$.$ Not enough information

Part D: Consider the CPU used in A alone. How does the average on$-$order $($pipeline$)$ inventory change if the demand variability for laptop A increases?

a$.$ Remains the same

b$.$ Increases

c$.$ Decreases

d$.$ Not enough information

Part E: The management has decided to use a generic CPU for both laptops A and B$.$ They wish to maintain a service level of $0\mathrm{.}8$ for this CPU. If the lead time L is still $5$ days, what will be the resulting base$-$stock level for this generic CPU? If your answer is not an integer, provide at least three decimal places, e$.$g$.,7\mathrm{.}500$

Part F: How did the total safety$-$stock inventory for CPUs for these two laptops change after the decision to use a generic CPU?

a$.$ Remains the same

b$.$ Increases

c$.$ Decreases

d$.$ Not enough information