# Service Levels of a datacenter, assigning probabilities

Hello people !

As a CIO, you have been supporting the computing and network services of business applications from 2 centers I and II. Suppose either center is capable of providing all of the service needs, that S1, S2>=0 is the level (quantity) of services delivered from each center and that the average costs of each per period is:

AC1=f(S1)=5S12 - 70 S1 + 300

and

AC2=f(S2)=SII2 - 32 S2 + 300

where the total service levels is S= S1+ S2

a) You have agreements totalling S=12. if you want to deliver services at min cosy, what quantities of services (S1 and/or S2) shud be delivered from each data center?

b)Suppose you have decided to shut one center and meet all service needs from only one. You also have enough information on the distribution of service levels per period. The probability density function of service levels per period is symmetric and unimodal with the probability of service levels

0<= P(S)<=1 and integral from 0 to inifinity of P(S) = 1

where P(S) is probability of service levels S

Write an equation for each center's avg cost that adjusts for the likelihood of all possible service levels. Since all services flow from one facility S1=S or S2=S ....

S= S1 (S2=0) OR S=S2 (S1=0)

c) Using result of b), Formulate and specify precisely a decision rule that wud determine whcih center wud continue to operate and which one wud be closed, where the decision criterion is to minimise cost of services.

ANY SUGGESTIONS APPRECIATED

J.M.