Balance sheets and income statements

Question 3

The following table illustrates excerpts from the balance sheets and income statements of two peer companies, A and B for a particular year. Evaluate these two companies’ cash to cash cycle (measured in days) and comment briefly on their relative performance on this dimension.

	Company A	Company B
Inventory	$500M	$900M
Accounts Receivable	$600M	$1000M
Accounts Payable	$400M	$600M
Revenues	$4000M	$7000M
Cost of Goods Sold	$2500M	$5200M

Question 4

Customers at a bank wait in a single line for the next available teller. Customer arrivals can be modeled by a Poisson distribution that has an average of 5 per hour. A teller can process an average of 10 customers per hour, which also can be modeled by a Poisson distribution (that is to say that the service time is exponentially distributed). If there is one teller on duty, determine:

• The average time a customer must wait in line.

• The average number of customers waiting in line.

• The average service time a customer takes.

• The probability that a customer will have to wait for service.

• The probability of no customers waiting in line.

Question 5

Suppose that an HMO system for processing pre-natal care and baby delivery insurance claims involves three primary steps (which we will call steps A, B, and C) in a sequential manner. Employees work in parallel on separate claims at each step.

The following table shows the number of employees working on each step, and the processing time per claim per employee.

Step	# of Employees	Time Required/Claim/Employee
A	40	10 minutes
B	20	4 minutes
C	30	6 minutes

• Find the total processing time, ignoring any waiting time, for an insurance claim.

• Find the capacity of each step and identify the bottleneck step(s). What is the capacity of the system?

• If all steps are working at exactly the bottleneck/capacity rate identified in (b), and the time in the system for all claims is equal to the total processing time identified in (a), how many claims, on average, are in the system?

Question 6

A local convenient store sells an evening paper, the Evening News. The owner of the store pays his supplier 40 cents a copy and sells the paper to his customers for 60 cents a copy. He estimates that the demand for the Evening News at his store is a normal distribution of mean 100 and standard deviation 25. The following three sub questions are independent from one another.

• Suppose that any unsold copies will be thrown away by the store at the end of the day. What is his optimal order quantity before knowing the actual demand?

• Suppose that the store owner has now negotiated with the supplier such that any unsold copies can be returned to the supplier, and he gets 25 cents back. However, the supplier also demands that he shares 5 cents of his profit for each sold copy. Under this new contract, what is the optimal order quantity for the store owner?

• Suppose that the store owner found another supply source of the same newspaper. Now, in addition to the newspapers he can buy from the original supplier at 40 cents each before demand is known, the owner can also buy an unlimited quantity of additional newspapers from the new supplier at 45 cents each after demand is known. What is the store owner’s optimal order quantity now from his original supplier? Suppose that any unsold copies will be thrown away by the store at the end of the day.