Alpha is deciding whether to invest $1 million in a project. There is a 70% chance that the project will be successful, yielding a return of 20% on investment. However, there is a 30% chance that the project will fail, in which case Alpha will only recover 80% of his investment.

1. What is the expected value of investing in the project?

2. Suppose Alpha evaluates the project in accordance with prospect theory. Specifi- cally,

v(x) = (x − r)^0.8 .if x ≥ r

−λ(r − x)^0.8 ,if r > x,

where λ > 1, r = $1 million is the reference point, and x is the amount of money received by Alpha at the end of the project. The corresponding probability weighting functions are such that γ = δ = 0.6.

(a) Argue (mathematically) that Alpha is loss averse.

(b) What is Alpha’s value of investing in the project if λ = 2?

(c) Find the value of λ such that Alpha is indifferent between investing and not investing in the project.

Beta’s boss assigns him a task on Monday which must be completed before Wednesday. The task takes a total of 10 hours. If Beta works on the task for Xt hours on day t, then he suffers a disutility of Xt^2 on day t. Throughout the problem t ∈ {1, 2, 3}, where 1 stands for Monday, 2 for Tuesday, and 3 for Wednesday. Beta’s time preferences are given by exponential discounting with the discount factor of δ = 0.8 per day.

1. What is the present value (as measured on Monday) of Beta’s disutility if he works for 6 hours on Monday and 4 hours on Tuesday?

2. Beta’s problem is to complete the task before Wednesday in such a way to minimize the present value of his distuility (as measured on Monday). Write down the mathematical version of Beta’s problem (that is, minimize some function subject to some constraint)

3. How many hours does Beta choose to work the task on Monday?

4. Now suppose that the boss wants to assign a new task to Beta on Tuesday and would therefore like Beta to have more time on Tuesday. She incentivizes Beta by offering him a reward of r3 = 10x1 on Wednesday if Beta works on Monday for x1 hours on the first task. How many hours does Beta choose to work on Monday?

BMI as a vital sign. Insured that all patients in local community clinics had their height and weight measured at each visit through provider education and training and referral system development (reached over 7,500 clinic patients). ? Breastfeeding policy. Implemented policies to promote breastfeeding in clinics, educated patients and clinic employees on the value of breastfeeding, and built capacity for more certified lactation specialists. Documented rates of exclusive breastfeeding from 7.7% in January 2005 to 20.2% in November 2009 (reached 900 staff and patients). ? School menu standards. Improved school meal/menu program during and after school to ensure meal compliance with nutritional standards and needs. Improved menu offerings and ingredients (e.g., added salad bars, changed to baked fries, whole wheat flour, etc). Expanded Universal Breakfast to five schools. Monitored compliance of policies for healthy fundraising, healthy vending, and alternative classroom rewards and incentives (reached over 7,700 students). ? PE standards. Implemented, at five elementary schools, the California standards-based physical activity curriculum and Game Days during school (reached 3,450 students). ? Worksite wellness. Worked with employers to adopt and implement worksite HEAL policies in the workplace; all county departments now have a worksite wellness coordinator. Received the worksite wellness bronze award for its accomplishments. (reached 4,000 employees in several worksites). ? Corner market produce. Implemented a grocery store Healthy Produce Basket project in neighborhood stores. Provided owners with educational materials and free produce in a basket and worked to identify ways to maintain the flow of produce. Some stores began purchasing from distributers. Worked with youth to provide free produce deliveries to these stores from unsold farmers’ market products to assist stores build a customer base for fresh fruits and vegetables (reached 4200 residents). ? Resident gardens. Local women from the Healthy Birth Outcome (HBO) Project grew produce in their backyards. Piloted selling excess produce at a stand in the park with the intention of creating a farmer’s market (reached 160 residents). ? Farmer's market. Organized and developed a four-month annual certified farmers’ market in West Modesto. Worked with Heifer International, a local organization that donated farm land and staff, and Project Uplift, a youth development project, to train youth to grow and sell organic produce with other vendors (reached 625 residents). ? After-school physical activity. Implemented a number of programs to increase the amount of exercise students get in afterschool programs, including the SPARK curriculum (offered daily), Powerplay (offered three times per week), and “Walk It Out” (offered three times per week). Increased daily after-school activity time from 15% to 45% (reached 1800 students). ? Walking school bus. Created a walking school bus at one school that increased the number of students walking approximately one half mile to school each day. Increased safety awareness through adult supervision, influenced traffic abatement, and reduced student tardiness (75 students walking daily). ? BMI counseling. Developed a routine counseling system to promote weight reduction among patients identified as being overweight in health care clinics (reached 140 patients). ? Youth awareness. Promoted student awareness of the importance of healthy eating and physical activity through the Educational Theater Program, Walk to School assemblies and other events (reached 2080 students). ? Community awareness of safe physical activity programs. Developed healthy messages for partners to insert into flyers, newsletters, bus ads, billboards, articles in local newspaper, and events (reached 17,000 residents). ? Worksite wellness promotion. Developed and implemented worksite wellness programs to decrease consumption of unhealthy foods and beverages and promote physical activity among employees. Received a state worksite wellness bronze award for its accomplishments (reached 4,000 employees in several worksites). After reading the description CAREFULLY, please organize the various objectives employed in this evaluation into the "bands" of the social-ecological model. You should briefly indicate WHY you feel these strategies fall within the specific categories of the model. From the list of objectives you have placed in the model, pick one objective from EACH of the "bands" of the model. Describe how you would evaluate that objective. Would you use formative or summative methods (and why)? What types of study design (qualitative or quantitative) and specific techniques would you use to collect the data in order to evaluate that objective? What sort of sampling might you use for each data collection approach? Remember to argue for your choices!

Select the substance with the larger standard state molar entropy from each of the following pairs and justify your answer (2 pts each):

(a)    Equal volumes of CO (g) at 2.0 bar pressure or 0.2 bar pressure

(b)    100% by volume chloroform (CHCl₃) or 5% by volume chloroform

(c)    Sodium iodide(aq) or sodium iodate(aq)

(d)    Pb(s) or P(s)

(e)    Ethanol(l) or methanol(l)

1. Obtain the equilibrium mole fractions (liquid and vapor) of a mixture of water, methanol and ethanol at 100 kPa and 70°C. You can assume the mixture is ideal.
2. Create one plot where the equilibrium mole fraction of benzene in the vapor phase is plotted against the equilibrium mole fraction of benzene in the liquid phase for three different pressures (0.2 bar, 0.6 bar and 1 bar). Comment on the effect of pressure on the relative volatility

A solid cylinder of 6 inch diameter and 4 inch high is compressed axisymmetrically to 2 inch high.
a) Calculate the final diameter of the product, the three orthogonal strains and the Von Mises strain.
b) Estimate the maximum total force required for this operation. Assume: coefficient of fricition 0.2; Use Ludwik's Law to find the pressure at maximum axial strain; the strength coefficient of the workpiece: K is 147 ksi, strain hardening exponent is 0.17.

A bubble-point feed mixture of 5 mol% A and 95 mol% B is to be distilled to obtain a distillate containing 35 mol% A and a bottoms containing 0.2 mol% A. The column has a partial reboiler and a partial condenser. If the constant relative volatility is given to be ?A,B = 6. Using graphical method, find out:

a) The minimum number of equilibrium stages.

b) The minimum boilup ratio: ??? /??

c) The actual number of stages if the boilup ratio is 1.2 times the minimum.

Suppose for a random sample of 49 CMU students, the mean amount of time spent eating or drinking per day is 1.58 hours with a S.D. of 0.62 hours!

a. What is the Standard Error of the estimate of the population mean?

b. What is the Margin of Error at a C.L. of 90%?

c. What is the right boundary of the C.I. at a C.L. of 90%?

d. At a 98% C.L., if the researcher wants to limit the error within 0.2 hours range, what size of the sample is needed?

With the aid of fourth order Runge-Kutta method, solve the competing species model defined by

dx/dt =x(2 − 0.4x − 0.3y), x(0) = 2

dy/dt =y(1 − 0.1y − 0.3x), y(0) = 4

where the populations x(t) and y(t) are measured in thousands and t in years. Use a step size of 0.2 for 0 ≤ t ≤ 2 and plot the trajectories of the populations with Matlab or GNU Octave.