AAAA... P4 ITS ECON

Problem 1 The purpose of this recitation is to familiarize students with a variety of integer programming modeling techniques as described in the IP Formulation Guide and in the powerpoint tutorial on IP formulations. We start with an integer program IP1 defined as follows: max 21x1 + 32x2 + 40x3 + 49x4 + 57x5 + +71x6 + 82x7 + 91x8 + 100x9 + 109x10 s.t.: 2x1 + 3x2 + 4x3 + 5x4 + rt depends on the parts preceding it. You do not need to repeat the integer programming objective or constraints given above. You may use the big M method for formulating constraint when it is appropriate. (a) (4 points) Write a single linear constraint that is equivalent to the statement "If x1 = 1, then x2 = 0." (b) (4 points) Write a single linear constraint that is equivalent to the statement "x2 = 1 or x3 = 0," but not both. (c) (4 points) Add a binary variable w1, and add two constraints that ensure that w1 = 1 if x5 + x6 70, and w1 = 0 if x5 + x6 69. (d) (4 points) Add 3 binary variables w2, w3, and w4 and at most 4 constraints so as to ensure that at least one of the following constraints is satisfied: (i) x5 92, (ii) x6 40, (iii) x7 + x8 74. (e) (4 points) Add a single binary variable w5 and two constraints to ensure that at least one of the following two constraints are satisfied (i) x9 45, (ii) x10 22. (f) (4 points) Add a single integer variable w6 and a constraint that ensures that x8 is divisible by 2 but not divisible by 4. (The remainder when dividing by 4 must be 2). (g) (4 points) Add three binary variables w7, w8, and w9 and two constraints that ensures that x10 = 13 or 39 or 88.

(h) (4 points) Add variable(s) and constraint(s) that model the cost of x4 as f4(x4), which is defined as follows: If x4 = 0, then f4(x4) = 0. If x4 1, then f4(x4) = 250 + 49x4. (i) (8 points) Add variable(s) and constraint(s) that model the cost of x5 as f5(x5), which is defined as follows: If 0 x5 10, then f5(x5) = 57x5. If 11 x5 20, then f5(x5) = 570. If 21 x5 100, then f5(x5) = 480 + 50x5. Problem 2 As the leader of an oil-exploration drilling venture, you need to determine which 5 sites out of 10 to evaluate for drilling opportunities. The goal is to select 5 sites with the lowest overall cost. Label the sites S1, S2, . . . , S10, and the exploration costs associated with each as c1, c2, . . . , c10. Regional development restrictions are such that: (i) Evaluating sites S2 and S7 will prevent you from evaluating either site S6 or S9. (ii) Evaluating sites S1 and S3 will prevent you from also evaluating both sites S5 and S6. (iii) Evaluating site S3 or S4 prevents you from evaluating site S6. (iv) Of the group S3, S6, S7, S8, at most two sites may be assessed. Formulate an integer program to determine the minimum-cost exploration scheme that satisfies these restrictions. Try to develop a model in which the only variables are x1, . . . , x10, where xj is 1 or 0 according as site j is evaluated or not. (For example, the constraint "Evaluating sites S2 and S7 will prevent you from exploring site S6" can be expressed as x2 + x6 + x7 2 because the only binary solutions prohibited have x2 = x6 = x7 = 1.)

Problem 3 Suppose you want to minimize or maximize a piecewise linear function of one variable, subject to linear constraints. This is a problem that can be solved by resorting to linear constraints only, possibly by adding extra variables. In this example, we consider the function with three pieces shown in Figure 1. (a) Suppose we want to minimize f(x) shown in Figure 1. Assume that x is subject to a set of linear constraints that involve other variables A(x' |x) = b, so that we cannot simply solve the problem by inspection because we do not know what values x will take. How can we formulate this problem in linear form? Do we need integer variables? (In your formulation, you can ignore the additional constraints A(x' |x) = b.) (b) Consider now the problem of maximizing f(x) of Figure 1, subject to a set of linear constraints that involve other variables. We cannot use the same approach of Part 2.A. Explain why and find an alternative way of formulating the problem, adding (binary or integer) variables as needed.

The state vector in the dynamic programming problem is identified as (k,61) but the role of begin ning of period capital is entirely captured through its effect on output. So use this to define the state vector as (v. 51). Then a Recursive Competitive Equilibrium is defined, in general, by three functions: c(vt, di), i (vi, dt), and q (ye, 61). (This is a cursory definition of a RCE. A complete answer would discuss the policy functions for the agent and how the relevant state variables are the individual and aggregate capital stocks, in addition to the & shock. Also a law of motion for the aggregate capital stock would be known by agents and, in equilibrium, there would be consistency between the agents and aggregate law of motion for the capital stock. Something along those lines would be more appropriate.) However, given the resource constraint, once the function for consumption is determined, then the investment function is also determined. And, due to eq.(1), the consumption function and production function also imply the equilibrium function for g (1,5t). So, more precisely, solving for the consumption function, c (t1,61), doen solve for the RCE. This task is made easier by the setup: it is reasonable, as we saw many times in class), to conjecture that this function is homogeneous of degree 1 in y. That is, c(vt, 6) = yew (de). If this conjecture is correct, then the necessary conditions will define w (51). Note that i (p, 61) = (1-w(5)) t and using this in eq (3) yields:

[2:32 PM, 10/31/2021] Flo: 1.1 Describe in detail the areas that you are required to monitor, as part of your council duties

Answer:

1.2 Explain in detail when, where and why you would conduct both routine and non-routine inspections

Answer:

1.3 List the approvals, licences or permits you would access when conducting inspections relevant to your council position and duties

Answer:

1.4 List and describe in detail the legislation that is relevant to your inspection duties

Answer:

Element 2: Identify, assess and act on areas of risk to the public and the environment

2.1 Describe and explain the process in place at your council to identify, assess and act on areas of risk related to the public and environments you monitor

Answer: ... [2:34 PM, 10/31/2021] Flo: Part. A - How are Epidemiologic Study Designs and Methods Applied to Public Health Practice:

1. What is the title of the manuscript you have been assigned? Who is the primary author of the article (i.e. the first author listed)?

2. What is the study design in the manuscript assigned to you and what are the primary characteristics of this particular study design?

3. Depending on the design of your assigned study how does this study design differ from the following designs: ecological, case-control, prospective cohort, retrospective cohort, cross-sectional?

4. What was the primary study research question? This is usually noted within the introductory section of a manuscript.

5. What appears to be the primary outcome that was investigated and analyzed? Were there additional outcomes that were examined? This might be mortality related to a specific disease, or the prevalence of a specific disease or health condition. Note whether there was only one outcome that was evaluated.

6. What appears to have been the study hypothesis in this study? Sometimes the research study question is a generalized statement but it is related to a background study hypothesis even if the hypothesis is not explicitly stated. Try to infer what the study authors hypothesized and note this in relation to the study question. (The hypothesis is considered to be a statement about the association between an exposure and an outcome (disease or illness) that is statistically testable. For example, in a study of alcohol consumption and breast cancer the investigators may have hypothesized that either alcohol consumption in general or high levels of alcohol may increase the risk of breast cancer. Although this is often in the Introduction, it may be explicitly stated in the Results or Discussion section.

7. How were study subjects (participants) recruited and how many subjects were enrolled in the study compared to how many actually participated in the study?

8. How were data collected for the study?

9. What was the main agent, exposure, or risk factor being investigated in relation to the outcome?

10. What types of covariates and confounders were evaluated? These are not the same as what is often referred to as the primary outcome or main effect. Remember a covariate or confounder is a variable that is thought to be relevant and important when evaluating the association of interest between a primary exposure or risk factor and the outcome. For example, alcohol consumption and the risk of breast cancer may be the primary association of interest for a study research question, but it will also be important to

consider other influential factors such as cigarette smoking, obesity, reproductive history, family history of breast cancer, etc. when evaluating this association.

Part B - How are Quantitative and Qualitative Methods Applied to Public Health Problems:

1. What quantitative and qualitative data collection methods were selected in this study? If qualitative methods were not used, please provide a brief narrative on what types of qualitative methods could have been selected for such a study.

a. "Revisiting the Quantitative-Qualitative Debate: Implications for Mixed-Methods Research" by Joanna E. M. Sale (2002)

b. "Qualitative Research in Epidemiology", by Susana Silva and Slvia Fraga (2012).

Part C - What Factors Affect a Population's Health:

1. What, if any, environmental risk factors were examined in the assigned manuscript?

a. Explain their relevance in relation to the study outcome, if examined.

b. Regardless of whether these factors were considered, find a publication (using PUBMED) that addresses the environmental factors associated with either the primary outcome in the assigned manuscript or an outcome of your choice.

c. Explain how environmental factors may affect a population's health.

2. What, if any, biological and genetic risk factors were examined in the assigned manuscript?

a. Explain their relevance in relation to the study outcome, if examined.

b. Regardless of whether these factors were considered, find a publication (using PUBMED) that addresses the biological and genetic factors associated with either the primary outcome in the assigned manuscript or an outcome of your choice.

c. Explain how biological and genetic factors may affect a population's health.

3. What if any behavioral and psychological risk factors were examined in the assigned manuscript?

a. Explain their relevance in relation to the study outcome, if examined.

b. Regardless of whether these factors were considered, find a publication (using PUBMED) that addresses the behavioral and psychological factors associated with either the primary outcome in the assigned manuscript or an outcome of your choice.

c. Explain how behavioral and psychological factors may affect a population's health.

4. What, if any, social, political, and economic risk factors were examined?

a. Explain their relevance in relation to the study outcome, if examined.

b. Regardless of whether these factors were considered, find a publication (using PUBMED) that addresses the social, political, and economic factors associated with either the primary outcome in the assigned manuscript or an outcome of your choice.

c. Explain how social, political, and economic factors may affect a population's health.

Part D - How Are Results Used to Advance Public Health Knowledge:

1. How did the authors of your assigned manuscript use statistics to describe and assess the specific populations being studied and to test their hypothesis?

2. With respect to the single most important finding in the study, what measure of association was calculated? (Relative Risk, Odds Ratio, Hazard Ratio, Correlation Coefficient, Regression Coefficient, Standardized Incidence Ratio).

3. What was the primary finding reported by the study authors and was it in keeping with what they anticipated? (i.e. Was their hypothesis supported by the results?).

4. What are the strengths and limitations identified by the authors of the study? This might range from strengths that are noted such as large study sample to limitations such as the possibility of particular forms of bias or small study sample size. The discussion of study strengths and limitations is usually toward the end of the manuscript in the 'Discussion' section.

5. How might the limitations impact the validity of the study and interpretation of the findings with respect to public health?

6. How well did the authors discuss whether this study would further advance understanding of the specific health condition and address gaps in knowledge and research?

7. What might be a future next step to take after conducting this study?

8. Overall, how would you interpret the results of their data analysis for impact on public health research?

9. How do you think the results of this study could be translated to public health policy and prevention of this disease or health problem

Prepare a table and line graph showing the unemployment and economic growth rate for a Caribbean country and a developed country (other than the US) for the last 5 years. Examine the relationship observed between the two countries.

b) Identify THREE public policies that can stimulate employment and facilitate economic growth in an economy.

Use examples to clearly illustrate how EACH policy can stimulate employment and facilitate economic growth in your country. [2:40 PM, 10/31/2021] Flo: Question: Explain your communication skills with members of the public when dealing with animals, in accordance with your council's policies on animal care and control and that you respond to complaints in a timely manner Answer:

Describe the circumstances when you are required, as part of your animal control duties, to be involved in effective community education programs

Answer:

Explain how you ensure your patrols are an effective means of capturing offending animals Answer:

Describe how you ensure you are working according to legislation (including the Companion Animals Act and Amendments, and Work Health and Safety Act), the council's procedures when capturing, impounding and releasing animals Answer:

What strategies do you undertake to ensure that you provide factual and legal information to animal owners at the time of infringements Answer:

What type of process do you follow when issuing impounding and warning notices to dog owners. Answer:

Describe the issues you take into account when deciding whether to impound or dispose of declared dangerous dogs. Explain how you ensure disposal is humane. Answer:

When investigating a dog attack, how do you ensure that the investigation is undertaken in such a way as to support possible court proceedings? Answer:

What is your council's process for registration checks, in accordance with council policy and legislation? Answer:

With whom do you liaise at council regarding the release or destruction of dogs, and/or pound/registration fees? Why are you required to consult them? Answer:

How do you ensure that all records are kept up-to-date? Answer:

Describe the process you follow when you intend to prosecute an offending animal owner. Answer:

What steps do you follow when the court proceedings find that the animal owner is guilty of an offence under the Companion Animal Act?