There are four separate questions, the maximal possible score is indicated below for each question. Please submit a single zip file identified by Your_Name_Your_Section.zip. This zip file will include a Word file with your personal Honor Code acknowledgement (copy the text highlighted above, type your name and RUID), your concise answers in the same Word file (without repeating the questions), and your Excel answer file[s] based on the exam template file[s] provided. Good luck! Question 1 10+10+10=30points You can use a copy of the Excel file Diet Planning, with appropriate modifications. Provide and document your entire answer within your file. (a) Your task is to plan a diet for the next 4 weeks for a person. During this time period, the overall nutritional value of the diet with respect to the vitamins considered (A,B1,B2,C) has to meet at least the minimum 28 -day requirement (2800% over the 4 weeks), without exceeding this requirement limit more than by its double (5600%). Set the minimal and maximal number of food packages over the 4 -week time period to 10 and to 40 , respectively. All other given data remain unchanged. Solve the model, and generate an answer report. (b) Next, assume that all food items considered should be provided in complete (non-fractional) packages. Provide a feasible solution. (c) Run Solver again, explicitly requiring that all food items considered should be provided in complete packages. Can you find an improved solution compared to the answer in (b)? If not, then how would you explain your finding? Question 25+5+10=20 points +10 bonus points for answering question 2.d A university exam consists of 30 multiple choice questions. Each question has five answer choices, with exactly one correct answer. A student, who is assumed to be completely unprepared for the exam, makes random "guesses" to answer each question. (a) How many questions should the student expect to answer correctly? (b) What is the standard deviation of the number of questions answered correctly? (c) What is the probability of answering at least 12 questions correctly? You don't have to calculate this probability numerically, just write down the corresponding formula in your answer. Based on your answers to (a) and (b), state whether this probability is relatively small or large. You can include a figure to support your argument. (d) Bonus question: Can you approximate the answer to question (c) using the central limit theorem? Question 35+5+5=15 points In a large class at a state university in the USA, the empirical probability distribution of students is summarized by the following table. We interpret the entries in this table as sufficiently close approximation of the "true" probability of random events. E.g., the probability of the event that a randomly selected student is an American woman is 0.40 . Denote by A,1,M, and W the events that a randomly chosen student is American, International, a Man, and a Woman, respectively. A student is chosen at random from this class. (a) Calculate the probability that the student chosen is American, given that the student is a Man. (b) Calculate the probability that the student chosen is Woman, given that she is International. (c) Calculate the probability that the student chosen is a Man, given that he is American. Question 435 points Consider the decision tree displayed below: it is based on a product development decision-making scenario analyzed by a medical technology development company. The company wants to decide whether to develop a new product further after developing it to a successful initial stage, or sell it in its current state to another company. Further development would lead to decisions to be made and random events that could occur with certain probabilities as shown by the decision tree. All dollar values are expressed in units of $1,000. Recall that we discussed similar problems in class: the decision tree structure and notation follows our related discussion: decision nodes are represented by square symbols (see nodes A, C, D), chance nodes are represented by circles (see nodes B, E, F, G, H, I). Based on the available information summarized by the decision tree, and applying the Bayesian decision making principle, the company wants to decide on the strategy to follow. You can "ignore" the narrative text written on the decision tree branches, just utilize the given terminal node payoff values and the event probabilities shown at the chance nodes. List the steps of your calculation in your Word document. What is the expected value of the optimal decision