A cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the urn follow a Poisson distribution at the rate of 4.0 per minute. In serving themselves, customers take about 12 seconds, exponentially distributed.

a.
How many customers would you expect to see on the average at the coffee urn?
b.
How long would you expect it to take to get a cup of coffee?
c.
What percentage of time is the urn being used?
d.
What is the probability that three or more people are in the cafeteria?
e.
If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 10 seconds, how does this change your answers to a and b?

Steele bicycle manufacturing company currently produces the handlebars used in manufacturing its bicycles, which are high-quality racing bikes with limited sales. steele produces and sells only 10,000 bikes each year. due to the low volume of activity, steele is unable to obtain the economies of scale that larger producers achieve. for example, steele could buy the handlebars for $31 each: they cost $34 each to make. the following is a detailed breakdown of current production costs: after seeing these figures, steele's president remarked that it would be foolish for the company to continue to produce the handlebars at $34 each when it can buy them for $31 each. calculate the total relevant cost. do you agree with the president's conclusion?

Fill in the missing words to correctly complete each sentence about analyzing a job posting. when reviewing a job posting, it’s important to check theto determine whether it’s worth your time to apply. if the post has been up for a while or it’s already closed, move on to the next position. if it’s still available, take note of when it closes so you’ll know when you mayfrom the company in regard to an interview.

Areal estate agent is considering changing her cell phone plan. there are three plans to choose from, all of which involve a monthly service charge of $20. plan a has a cost of $.42 a minute for daytime calls and $.17 a minute for evening calls. plan b has a charge of $.52 a minute for daytime calls and $.15 a minute for evening calls. plan c has a flat rate of $80 with 275 minutes of calls allowed per month and a charge of $.38 per minute beyond that, day or evening.a. determine the total charge under each plan for this case: 150 minutes of day calls and 70 minutes of evening calls in a month. (do not round intermediate calculations. round your answer to 2 decimal places. omit the "$" sign in your response.)c. if the agent will use the service for daytime calls, over what range of call minutes will each plan be optimal? (round each answer to the nearest whole number.include the indifference point itself in each answer.)d. suppose that the agent expects both daytime and evening calls. at what point (i.e., percentage of total call minutes used for daytime calls) would she be indifferent between plans a and b?