SECTION A: Multiple Choice and True/False
Provided Dollar amounts in the decision tree are in millions.
1) Which of the following is a decision node? A) whether or not clinical trials are successful B) whether or not to seek FDA approval C) whether the market is large, medium, or small D) whether or not FDA approved
2) What is the probability that the drug reaches to a large market? A) 0.054 B) 0.700 C) 0.108 D) 0.018
3) Which of the following best defines payback period? A) It is the number of time periods before the net expenditure exceeds the amount of the initial investment. B) It is the number of time periods before the amount of the initial investment exceeds the cash inflows of a proposed project. C) It is the number of time periods before the cash inflows of a proposed project exceed the amount of the initial investment. D) It is the number of time periods before the cash inflows of a proposed project equal the amount of the initial investment.
Use the below payoff table with four mortgage options to answer question 4:
4) Which of the following decisions has the best average payoff? A) 1-year ARM B) 30-year fixed C) 3-year ARM D) 5-year ARM
5) In linear optimization models, an objective function is the . A) unknown value that the model seeks to determine B) limitation or requirement that decision variables must satisfy C) set of values that satisfies all the constraints D) quantity that we seek to minimize or maximize
6) An optimal solution is . A) the limitation or requirement that decision variables must satisfy B) also known as the constraint function C) the quantity that we seek to minimize or maximize D) any set of decision variable values that maximizes or minimizes the objective function
7) The is the difference between the right- and left-hand sides of a constraint. A) shadow price B) slack C) optimal solution D) allowable increase
8) Integer linear optimization models differ from nonlinear optimization models in that integer linear optimization models . A) contain terms that cannot be written as constant times a variable B) contain some or all variables that are restricted to being whole numbers C) use only equalities to describe the constraints D) use only inequalities to describe the constraints
9) What is Monte Carlo simulation? A) It is a ratio of the departure of an estimated parameter from its notional value and its standard error. B) It is a measure of the correlation between two variables X and Y that falls exclusively between the values +1 and -1. C) It is the process of generating random values for uncertain inputs in a model, computing the output variables of interest, and repeating this process for many trials in order to understand the distribution of the output results. D) It is an approach for developing a comprehensive understanding and awareness of the risk associated with a particular variable of interest.
10) Risk analysis seeks to examine the impacts of uncertainty in the estimates and their potential interaction with one another on the output variable of interest. True or False?
SECTION B: Linear Optimization Modeling
Problem: Burger Office Equipment produces two types of desks: standard and deluxe. Deluxe desks have oak tops and more expensive hardware and require additional time for finishing and polishing. Standard desks require 80 sq. ft. of pine and 10 hours of labor, while deluxe desks require 60 sq. ft. of pine, 18 sq. ft. of oak, and 16 hours of labor. For the next week, the company has 5,000 sq. ft. of pine, 750 sq. ft. of oak, and 400 hours of labor available. Standard desks net a profit of $150, while deluxe desks net a profit of $320. All desks can be sold.
1) Develop a linear mathematical optimization model to determine how many of each desk the company should make next week to maximize profit contribution.
2) Implement your model on a spreadsheet and find an optimal solution using Solver.
3) Explain the reduced cost associated with standard desks.
4) What constraints are binding?
5) If 25% of the oak is determined to be cosmetically defective, how will the optimal solution be affected?
6) The shop supervisor has suggested that his workers be allowed to work an additional 50 hours at an overtime premium of $12/hr - is this a good idea? Why or why not?
SECTION C: Monte Carlo Simulation
Problem: Suppose an employee starts working after completing her MBA at age 30 at a starting salary of $50,000. She expects an annual salary increase to be at minimum 1%, at maximum 5%, with a uniform distribution. Her retirement plan requires that she contribute 8% of her salary, and her employer matches that by adding an additional 35% of her contribution. She anticipates an annual return on her retirement portfolio (i.e., return on investment) to be a normal distribution with a mean of 4% and standard deviation of 3.5%. She plans to retire at age 60. Create a spreadsheet model to forecast her average return on investment (i.e., retirement account balance) when she retires at age 60 based on 5,000 simulation trials.
1) What is the expected average balance of her retirement account when she retires at age 60?
2) What is the probability that her ending retirement balance at age 60 will be over $450k? Generate a histogram or density chart that shows this.