1. Your regular tennis partner has offered a friendly wager to you. The two of you will play out one point in which you can serve. The loser pays the winner $100. If your first serve is not in play, you get a second serve. If your second serve is not in play, you lose the point.
You have two kinds of serves: a hard one and a soft one. You know that your hard serve is in play 65% of the time and, when it is in play, you win the point 75% of the time. You put your soft serve in play 88% of the time and, when it is in play, you win the point 27% of the time.
Construct a Decision Tree for this problem and answer the following questions:
1. Should you accept the wager?
2. What is the Expected Monetary Value?
3. If so, should you use your hard or soft serve?
2.
|
Income
|
Probability
|
|
$850
|
0.35
|
|
$900
|
0.25
|
|
$950
|
0.25
|
|
$1,000
|
0.15
|
A graduate student has variable income from his assistanceship and tutoring work. He extimates his monthly income (as of the beginning of the month) to follow follow this distribution:
Income Probability
$850 0.35
$900 0.25
$950 0.25
$1,000 0.15
His monthly expenses are expected to range from $850 to $1,200, following a uniform distribution.
He has a beginning cash balance in September of $1,500.
1. What is his expected cash balance at the end of the following May?
2. What is the probability that his balance will be negative in one or more month?
3. What is the probability that his May ending balance is less than $500?
3. Fred's Fasteners is a manufacturing company that has decided they are large enough to choose to be self-insuring for employee health insurance. The Chief Financial Officer has asked for some projections on the costs to the company for the next fiscal (also a calendar) year. Analysts studying records for prior periods have decided on the following assumptions.
January employment level will be 9,250, and is expected to increase in subsequent months by a percentage randomly chosen from a uniform distribution, minimum of -2%, maximum of 4%
Each emplyee will contribute $325 per month. This is fixed for the year.
Payable health care benefits (costs) for the program will be about $625 for January but will rise by a randomly determined percentage that is normally distributed with a mean value of 0.4% and standard deviation of 0.15% each month from the prior month.
There is also a processing cost of $75 per month per employee paid to Blue Cross who will be handling the claims processing.
1. What is the Expected cost to the company for next year?
2. The CFO wants to set a budget amount that we have a confidence level of 85% that we won't go over budget. What figure should be used?
3. What is the highest company cost found in the simulations?
4.
|
Demand
|
Probability
|
|
15
|
0.08
|
|
20
|
0.12
|
|
25
|
0.25
|
|
30
|
0.20
|
|
35
|
0.20
|
|
40
|
0.15
|
The Paris Bakery has decided to bake 30 batches of its famous beignets at the beginning of the day. The store has determined that daily demand will follow the distribution shown in the following table:
Demand Probability
15 0.08
20 0.12
25 0.25
30 0.20
35 0.20
40 0.15
Each batch cost the Paris Bakery $50 and cxan be sold for $100. The Paris Bakery can sell any unsold batches for $25 the next day.
1. What is the Expected profit for one month (25 days) of operation?
2. Investigate the profitability that would result if instead of baking 30 batches each morning, they bake 25, 30, 35, or 40 batches. Which would you recommend and why? (You should use Decision Table with Crystal Ball, or Scenario Manager if plain Excel.)