Practice Final 2

1. Consider a hospital with 2 operating rooms dedicated to the ER.  Operations take an average of 1.5 hr each.  What is the largest arrival rate of new cases such that the waiting time is less than 10 min with 90% probability?  Assume it a M/M/s queue.

2. Would your answer to problem 1 increase or decrease if the standard deviation of the length of an operation increased?

3. What three pieces of information would you need to make a recommendation to the bookstore about how many copies they should order of a textbook for a particular class?

4. Consider the following optimization problem,

min sum_i IF(xi>0,1,0)
s.t.	| A x - b | <= 1
	5 >= xi >= 0 for all i

Where x and b are vectors and A is a matrix.
Here x is the decision variables.
a) Find an equivalent formulation that does not use an IF statement, but instead uses some binary variables in a linear fashion.
b) Find an equivalent formulation that replaces the absolute value with a set of linear constraints.

5. A store has 5 customer service representatives handling 10 customers an hour on average.  Each can handle a problem in 15 minutes on average.  20% of customers are not happy with the outcome and then ask to speak to the supervisor.  The supervisor handles a complaint in 7 minutes on average. 
a) What is average time the supervisor spends handling complaints?
b) What is the average time a customer spends at the store until his complaint is resolved?