Acompany has positions for three employees. applicants for these jobs appear at a poisson rate of two per year. if all jobs are filled, they look elsewhere. those who hold a job do so for an exponentially distributed time with mean one-half year. a. determine the proportion of applicants that are turned away. b. what is the average number of employees?

Answer and Explanation:

Let πj denote the steady-state probabilities. Assume that these values are known.

a). Determine the proportion of applicants that are turned away.

Because Poisson arrivals see time averages (PASTA), the proportion of applicants that are turned away is equal to the fraction of the time that the company is fully staffed.

Therefore, π3 ←

b). What is the average number of employees?  

From the definition of expected value, 0π0 + 1π1 + 2π2 + 3π3 ←

$90,000

Explanation:

Data provided in the question:

Net cash provided by operating activities = $430,000

Average current liabilities = $300,000

Average long-term liabilities = $200,000

Dividends paid = $120,000

Capital expenditures = $220,000

Purchase of treasury stock = $22,000

Payments of debt = $70,000

Now,

Trent's Free cash flow

= Net cash provided by operating activities - Capital expenditures - Dividends paid

= $430,000 - $220,000 - $120,000

= $90,000