need help with discussions
1) What are the main advantages of using a networkbased approach to project management rather than a Gantt chart? Under what circumstances might a Gantt chart be preferable to a networkbased approach?
2) consider the two capacity options for Arktec manufacturing from Problem 2 and the three possible demand scenarios from Problem 4. First, draw the decision tree for Arktec Manufacturing. When drawing your tree, assume that managers must select a capacity option beforethey know what the demand level will actually be. Then, calculate the expected value for each decision branch. Which option would you prefer and why?
*Text book material is attached below for problem 2
PROBLEMS
(* = easy; ** = moderate; *** = advanced)
Problems for Section 6.3: Methods of Evaluating Capacity Strategies
1. (*) The Shelly Group has leased a new copier that costs $700 per month plus $0.10 for each copy. What is the total cost if Shelly makes5,000 copies a month? If it makes 10,000 copies a month? What is the percopy cost at 5,000 copies? At 10,000 copies?
2. Arktec Manufacturing must choose between the following two capacity options:
FIXED COST (PER YEAR) 
VARIABLE COST (PER UNIT) 

Option 1 
$500,000 
$2 per unit 
Option 2 
$100,000 
$10 per unit 
a. (*) What would the cost be for each option if the demand level is 25,000 units per year? If it is 75,000 units per year?
b. (**) In general, which option do you think would be better as volume levels increase? As they decrease? Why?
c. (*) What is the indifference point?
3. (*) Suppose the Shelly Group has identified two possible demand levels for copies per month:
COPIES (PER MONTH) 
PROBABILITY 
5,000 
50% 
10,000 
50% 
What is the expected cost if it costs $700 per month to lease a new copier and the variable cost is $0.10 for each copy?
4. Consider the two capacity options for Arktec Manufacturing shown below:
FIXED COST (PER YEAR) 
VARIABLE COST (PER UNIT) 

Option 1 
$500,000 
$2 per unit 
Option 2 
$100,000 
$10 per unit 
Suppose the company has identified the following three possible demand scenarios:
DEMAND (UNITS PER YEAR) 
PROBABILITY 
25,000 
30% 
60,000 
40% 
100,000 
30% 
a. (**) What is the expected value of each option? Which option would you choose, based on this information?
b. (**) Suppose the lowest and highest demand levels are updated to 40,000 and 110,000, respectively. Recalculate the expected values.What happened?
c. (**) Draw the decision tree for Arktec Manufacturing. When drawing your tree, assume that managers must select a capacity option before they know what the demand level will actually be.
d. (**) Calculate the expected value for each decision branch. Which option would you prefer? Why?
5. You are the new CEO of Dualjet, a U.S. company that makes premium kitchen stoves for home use. You must decide whether to assemblethe stoves inhouse or to have a Mexican company do it. The fixed and variable costs for each option are as follows:
FIXED COST 
VARIABLE COST 

Assemble inhouse 
$55,000 
$620 
Contract with Mexican assembler 
$0 
$880 
a. (**) Suppose DualJet’s premium stoves sell for $2,500. What is the breakeven volume point for assembling the stoves inhouse?
b. (*) At what volume level do the two capacity options have identical costs?
c. (**) Suppose the expected demand for stoves is 3,000. Which capacity option would you prefer, from a cost perspective?
6. Emily Watkins, a recent college graduate, faces some tough choices. Emily must decide whether to accept an offer for a job that pays$35,000 or hold out for another job that pays $45,000 a year. Emily thinks there is a 75% chance that she will get an offer for the higherpaying job. The problem is that Emily has to make a decision on the lowerpaying job within the next few days, and she will not knowabout the higherpaying job for two weeks.
a. (**) Draw out the decision tree for Emily Watkins.
b. (**) What is the key decision Emily faces? What is the expected value of each decision branch?
c. (**) What other factors might Emily consider, aside from expected value?
7. Philip Neilson owns a fireworks store. Philip’s fixed costs are $12,000 a month, and each fireworks assortment he sells costs, on average,$8. The average selling price for an assortment is $25.
a. (*) What is the breakeven point for Philip’s fireworks store? Suppose Philip decides to expand his business. His new fixed expenseswill be $20,000, but the average cost for a fireworks assortment will fall to just $5 due to Philip’s higher purchase volumes.
b. (*) What is the new breakeven point?
c. (**) At what volume level is Philip indifferent to the two capacity alternatives outlined above?
8. Merck is considering launching a new drug called Laffolin. Merck has identified two possible demand scenarios:
DEMAND LEVEL 
PROBABILITY 
1 million patients 
30% 
2 million patients 
70% 
Merck also has the following information:
Revenue 
$140 per patient 
Fixed costs to manufacture and sell Laffolin 
$70 million 
Variable costs to manufacture and sell Laffolin 
$80 per patient 
Maximum number of patients that Merck can handle 
3 million 
a. (*) How many patients must Merck have in order to break even?
b. (**) How much money will Merck make if demand for Laffolin is 1 million patients? If demand is 2 million patients?
c. (**) What is the expected value of making Laffolin?
d. (**) Draw the decision tree for the Laffolin decision, showing the profits for each branch (Total revenues – total variable costs – totalfixed costs) and all expected values.
9. Clay runs a small hot dog stand in downtown Chapel Hill. Clay can serve about 30 customers an hour. During lunchtime, customersrandomly arrive at a rate of 20 per hour.
a. (*) What percentage of the time is Clay busy?
b. (*) On average, how many customers are waiting to be served? How many are in the system (i.e., waiting and being served)?
c. (*) On average, how long will a customer wait to be served? How long will a customer be in the system?
10. Peri Thompson is the sole dispatcher for Thompson Termite Control. Peri’s job is to take customer calls, schedule appointments, and insome cases resolve any service or billing questions while the customer is on the phone. Peri can handle about 15 calls an hour.
a. (*) Typically, Peri gets about 10 calls an hour. Under these conditions, what is the average number of customers waiting, and what isthe average waiting time?
b. (**) Monday mornings are unusually busy. During these peak times, Peri receives around 13 calls an hour, on average. Recalculate theaverage number of customers waiting and the average waiting time. What can you conclude?
11. Benson Racing is training a new pit crew for its racing team. For its first practice run, the pit crew is able to complete all the tasks inexactly 30 seconds—not exactly worldclass. The second time around, the crew shaves 4.5 seconds off its time.
a. (*) Estimate the learning rate for the pit crew, based on the times for the first two practice runs.
b. (**) Mark Benson, owner of Benson Racing, says that the pit crew must be able to complete all the tasks in less than 15 seconds inorder to be competitive. Based on your answer to part a, how many times will the pit crew need to practice before it breaks the 15second barrier?
c. (**) Is it realistic to expect the pit crew to experience learning improvements indefinitely? Explain.
12. Wake County has a special emergency rescue team. The team is practicing rescuing dummies from a smokefilled building. The first time,the team took 240 seconds (4 minutes). The second time, it took 180 seconds (3 minutes).
a. (*) What is the estimated learning rate for the rescue team, based on the information provided?
b. (**) Suppose that the team’s learning rate for the rescue exercise is 80%. How many times will the team need to repeat the exerciseuntil its time is less than 120 seconds (50% of the original time)?
c. (**) How long will it take the emergency team to perform its 20th rescue if the learning rate is 80%?
13. After graduating from college, your friends and you start an Internet auction service called TriangCom. Business has been fantastic, with10 million customer visits—or “hits”—to the site in the past year. You have several capacity decisions to consider. One key decisioninvolves the number of computer servers needed. You are considering putting in 10, 20, or 30 servers. Costs and capacity limits are asfollows:
NUMBER OF SERVERS 
FIXED COST PER YEAR 
VARIABLE COST PER HIT 
MAXIMUM HITS PER YEAR 
10 
$50,000 
$.005 
20 million 
20 
$90,000 
$.003 
40 million 
30 
$120,000 
$.002 
60 million 
In addition, marketing has developed the following demand scenarios:
YEARLY DEMAND 
PROBABILITY 
15 million hits 
30% 
30 million hits 
60% 
45 million hits 
10% 
Finally, TriangCom generated $5 million last year, based on 10 million hits. Put another way, each hit generated, on average, $0.50 inrevenue.
a. (**) Calculate the breakeven point for each capacity alternative.
b. (**) At what demand level will you be indifferent to having either 10 or 20 servers?
c. (***) Calculate the expected value for each capacity alternative. (Hint: Don’t forget about capacity constraints that can limit the numberof hits each capacity alternative can handle.) Which alternative will you prefer if you want to maximize the expected value?
TriangCom has hired Donna Olway to code programs. Donna completes her first job in five weeks and her second job in four weeks.Assume that (1) Donna continues to learn at this rate and (2) her time improvements will follow a learning curve.
d. (**) How long will you expect Donna to take to complete her sixth job?
e. (**) How long will you expect Donna to take to complete the next five jobs (jobs 3 through 7)?
With thousands of customers, TriangCom has established a hotline to take customer calls. The hotline is staffed by one person 24 hours aday. You have the following statistics:
Service rate for calls 
15 per hour, on average 
Arrival rate for calls 
11 per hour, on average 
As part of your customer service policy, you have decided that the average waiting time should not exceed 2.5 minutes.
f. (*) What is the average number of callers being served?
g. (*) On average, how many callers are waiting to be served?
h. (**) What is the average waiting time for a customer? Is this time acceptable, given the customer service policy?
14. Rich Sawyer runs a landscaping firm. Each year Rich contracts for labor and equipment hours from a local construction company. Theconstruction company has given Rich three different capacity options:
CAPACITY OPTION 
LABOR HOURS 
EQUIPMENT HOURS 
High capacity 
9,000 
6,000 
Medium capacity 
6,750 
4,500 
Low capacity 
4,500 
3,000 
Cost per labor hour: 
$10 per hour 
Cost per equipment hour: 
$20 per hour 
Once Rich has chosen a capacity option, he cannot change it later. In addition, the cost for each capacity option is fixed. That is, Rich mustpay for all labor and equipment hours he contracts for, even if he doesn’t need them all. Therefore, there are essentially no variable costs.Rich also has information concerning the amount of revenue and the labor and equipment hours needed for the “typical” landscapingjob:
Job revenue 
$2,000 per job 
Labor hours per job 
30 hours 
Equipment hours per job 
20 hours 
Finally, Rich has identified three possible demand levels. These demand levels, with their associated probabilities, are as follows:
DEMAND LEVEL 
NUMBER OF JOBS 
PROBABILITY 
High demand 
300 
30% 
Medium demand 
200 
40% 
Low demand 
120 
30% 
a. (***) Determine the total fixed costs and the breakeven point for each capacity option. What is the maximum number of jobs that can