Pre-Course Final Exam 2011


This is a draft of the final exam for this course. Each question or cluster of question has an expandable list of skills you will be responsible for acquiring and can expect to be examined on. This pre-test is intended to give us a baseline against which we can measure progress as well as to give you an idea of what is to come.

Answer the following questions to the best of your current ability. Feel free to use the answer "I have no idea." Check your solutions/answers against those given here (for most questions) and submit only a report of how you did on each question. Categories are CORRECT, INCORRECT. If incorrect indicate what you got wrong if close or just indicate "did not know how to do"

Final Exam

What is a Model? What is Simulation?

Generic Concepts

1. Name seven "modeling" techniques discussed in this course (not the little details inside of a technique, but the big seven tools).

Which of the following represent linear processes?

2. One youth agency is estimated to be able to reduce delinquency by 15%. Two agencies would be able to reduce it by 27%, three by 37%, and five agencies by 50%.

3. We predict that 25 people will show up at the protest no matter what. Further, all of our research shows that for each $100 we spend in public relations and networking, we can expect 12 more people to show up.


8. What is an OBJECTIVE FUNCTION and when do we encounter it?

9. What is the difference between a stable and an unstable equilibrium?

9. Label each of the following as representing either stable or unstable equilibria.



Word Skills

Flow Chart Skills

1. Sketch a flowchart that represents this bit of logic: “if you are a woman then if you are over 40 you should have this test no matter what but if either parent had diabetes women should have the test no matter what. Men only need to take the test if they are overweight.”

11. No Question

12. No Question

13. March & Lave describe the "act of modeling" as being composed of the following "steps." Observe a pattern. Describe a process that could produce an observed pattern. Predict what else that process would produce. Put these into this flow chart and write a short paragraph describing their general process of model building as an explanatory endeavor.


Decision Trees

* choice/chance

  • exhaustive/mutually exclusive
  • folding-back
  • imperfect tests
  • risk-aversion
  • the value of information
  • utility theory

14. Identification: CHANCE/CHOICE NODE.

15. Identification: EXPECTED VALUE.

16. Consider this decision chart about whether or not to use a new training curriculum at the city's firefighter academy. Its developers make claims that it produces better trained firefighters in less time and at less cost. Your experts think there's about a 50:50 chance that it performs as well as claimed. You've estimated that the net benefit of the old, traditional training approach is 5 while the savings and better training promised with the new curriculum would be worth 8. If however, it turned out not to work, then the cost of retraining would bring the total benefit down to 3. Fortunately you have the option of doing a pilot test at cost T to determine whether the new training methods work well or not. This information is laid out in a decision tree. Explain how to read the tree and what we should do.


Charts, Tables, and Diagrams

Cost/Benefit Analysis

CBA Cost-Benefit Analysis




20. An Oakland youth oriented non-profit is considering building a new headquarters. Funding is all lined up. The building being considered will cost 1.75 million. The net savings in rent and utilities and such over the years net out to 1.5 million. Maintenance on the new building is expected to be 750,000 over the period in question. Should they go ahead with the project?

21. City officials are considering four different approaches to relieving pressure on the local housing market. Cost estimates for four projects A, B, C, and D have been obtained. For each project experts have also estimated the expected benefits in terms of taxes, savings on services, etc. How would you start to think about this? What else would you want to know?


Discounting Skills List

22. What is the basic equation for compound interest. Let $P$ be the principal and $R$ be the interest rate per period and $t$ the time in periods.

23. DEFINE internal rate of return.

24. Lots of talk recently about green this and green that. Homeowners, cities, counties, states and the federal government all have to figure out whether to invest in green technologies of various kinds. Typically these things have big up front costs and relatively long pay back periods. How does one best think about which ones make sense?

25. We must choose between two energy saving projects. For each one we have data on how long it will take to install, what the payment schedule will be and how much each will let us save over the years along with projected maintenance costs.

Multiple Attributes Problems

26. Consider the following rankings of several alternative projects under consideration at your agency. Cheaper is better. High political attractiveness is better. Higher effectiveness is better.
Alternative Cost Political Attractiveness Actual Effectiveness
Option A 100 Not 84
Option B 300 Not 67
Option C 300 High 49
Option D 200 Medium 93

a. Is any option strictly dominated by another? D»B. A>=B.
b. Suppose Cost is more important than political attractiveness is more important than effectiveness. Give a lexicrographic ordering of the alternatives. A > D > C > B
c. Suppose we are satisficing and our standards are: it has to cost less than 300 and at least a little bit politically attractive. What are our choices? D
d. Suppose we have an objective function that goes like this:
Rank options on each factor. In the case of ties, split the sum (i.e., a tie for 2nd place would split 2nd and 3rd and each would get 2.5). Add up the point scores.
What option do we choose?

Randomness as a Tool: Random Experiments and Monte Carlo Simulation

27. If a group of monkeys took the GRE, what do we expect their average score would be? Make any necessary assumptions and explain your reasoning.

28. When building computer models, why do we sometimes use random numbers that are normally distributed, sometimes uniformly distributed, and sometimes coming from a special distribution such as the Poisson distribution?

Stock & Flow Models

29. Suppose you have been put in charge of establishing an "army" of community organizers as a part of a new Obamanization of American Communities. The goal is to have a steady state program size of 800,000 organizers. Our program involves a recruitment phase, a training phase, a placement phase and an active duty phase. Recruitment happens continuously with training academies starting every 6 months. The training itself lasts 6 months and is followed by a 6 month placement rotation, and then a year of active duty volunteer work.

We will assume that logistics and such are taken care of and we are only interested in building a model that will help us to see how recruitment and retention rates are related to the the number of volunteers on the street at any given point.

During training we expect 25% of recruits to drop out. A further 10% will leave during the placement phase. Once organizers get to active duty status we expect 100% retention for one year. At the end of one year, about 30% of organizers sign up for one more year of active duty.

First describe the situation in words. If the program begins with 100,000 recruits on 1 January 2011, what will the first few half-years look like in terms of activity?

Explain what this diagram shows and what sorts of equations we would associate with it (based on the above information).


Project Management

30. Consider this PERT chart illustrating the process of designing an airplane. In each box you will see the number of days we expect the subprocess to take (ET) and the longest amount of time it can be expected to take with delays and problems and such. How long do we expect the process to take from start to finish?


Back of the Envelope Calculations

31. What is the order of magnitude of the number of seconds in a year (show your reasoning).

32. If there are about 36 million people in California, about how many school age children are there? Show your reasoning.

Markov Models

33. What is the eigen vector of a Markov model?

34. A criminologist and an activist decide to collaborate on a project designed to reduce prison population. In the spirit of starting simple, they identify 4 states in which people can find themselves: never imprisoned; incarcerated; on parole; post-parole. The period of time in their analysis will be one year. Suppose 70% of the population has never been incarcerated. Each year 2% of these people are imprisoned. Of those currently incarcerated, 5% are released each year onto parole. Average parole is 5 years so that a person on parole has a 20% chance of finishing parole. Those on parole have a 10% chance of finding themselves back in prison in any given year. Individuals who are post parole have a 4% chance of returning to prison in any given year.

35. Look at this diagram about the fate of mortgages and tell us what happens to mortgages that are late. Explain what these figures and tables are and interpret what they mean.


36. You have been assigned to assess a social services project meant to address the "continuum of care" around family homelessness. The continuum of care concept is based on the idea that in a problem like homelessness affected persons pass through stages both on the way into and out of the problem. At different stages, different services are needed (e.g., a homeless family needs emergency shelter NOW; a family living in a shelter needs resources and contacts to enable them to move into transitional housing; a family in transitional housing may need help assessing what kind of permanent housing is appropriate to their situation; a family teetering on the edge of losing its home may need mortgage support). Traditionally, agencies specialize in particular stages and may not collaborate at all with agencies concerned with other stages.

Your client has a simple request. It wants to build a picture of "the problem" and the stages that families pass through on the into and out of homelessness. They have categorized some of the stages:

  • Pre-at-risk families who are currently doing well but who could themselves at risk with the loss of a job or other unanticipated circumstance. We think of these families as "pre-at-risk" and there are services targeted at "risk prevention" – educating homeowners about re-finance options, renters' legal aid, etc.
  • Families at risk of homelessness. Families currently with a home but at risk for losing the home due to foreclosure or because of behavioral problems (drugs, etc.) on the part of adults in family.
  • Currently Homeless Families. Families currently living "on the street."
  • Emergency Shelter Families. Short term, safe and decent shelter provided as an alternative to the streets. Families currently staying in emergency shelters. Time in shelters varies depending on, among other things, availability of staff to assist in placements in transitional housing and the availability of transitional housing.
  • Families currently in transitional housing. Families who have moved out of emergency shelters but have not found permanent housing. The program here consists of training and assessment. Training is about financial management, job skills, employment finding, etc. The assessment is to determine whether on-going support will be needed to help these families succeed.
  • Families in permanent housing. Client families who have been placed in permanent (usually rental) housing. Ongoing services such as those mentioned above under "pre-at-risk" are often appropriate on an ongoing basis for these families.
  • Families in permanent supportive housing. Families in need of special services to make their continued tenure in permanent housing viable. These include services such as education, employment assistance, health care, substance abuse treatment and mental health care, child care, and transportation.

What kind of a model would you suggest building?

Queuing Models

37. Explain the basic idea of "waiting time as deadweight loss."

38. WHAT KIND OF MODEL? The DMV is mindful of its poor reputation for service. You are employed as a consultant to help them deal with it. In particular, they are trying to figure out whether some sort of appointment system will be effective both in terms of customer satisfaction and overall productivity.

39. El Oakalo, CA is a small town with a beautiful new public aquatics facility with a great pool and very nice surrounding areas. Since it was built with taxpayer money, it's free to town residents. Unfortunately, there's not a lot to do in town and so everybody shows up — even folks who have no interest in swimming and just want to sit around under beach umbrellas. Regulations restrict the number of people on site to 575 and this means that lots of swimmers face big delays before they can get in the pool. Help!

40. No question

41. No question

Agent Models

42. No question.

43. No question.

44. No question.

Linear Programming

45. You are working for an agricultural cooperative which is helping local farmers figure out how to optimize the mixture of crops they plant. A typical farmer has 10 acres to plant in wheat and rye. She has to plant at least 7 acres. However, she has only the equivalent of $1200 to spend and each acre of wheat costs $200 to plant and each acre of rye costs $100 to plant. Moreover, the farmer has to get the planting done in 12 hours and it takes an hour to plant an acre of wheat and 2 hours to plant an acre of rye. If the expected profit is $500 per acre of wheat and $300 per acre of rye how many acres of each should be planted to maximize profits?

46. A non-profit supplier of after-school materials has orders for 600 copies from San Francisco and 400 copies from Sacramento. The organization has 700 copies in a warehouse in Novato and 800 copies in a warehouse in Lodi. It costs $5 to ship a text from Novato to San Francisco, but it costs $10 to ship it to Sacramento. It costs $15 to ship from Lodi to San Francisco, but it costs $4 to ship it from Lodi to Sacramento. How many copies should the organization ship from each warehouse to San Francisco and Sacramento to fill the order at the least cost?

47. No question.

Difference Equations

48. Every year 10 percent of the public housing units in Oakfrisco deteriorate to the point where they are uninhabitable and must be demolished. Current plans and budget constraints call for the construction of 800 new units per year. Is there an equilibrium number of housing units? Is it a stable equilibrium?

49. Based on what we have learned about how the slope affects the type of equilibrium, draw arrows on the black line in this diagram to indicate where the system would go in the four labeled sections. Describe a situation that this diagram might represent.