Solve the following graphically: Minimize 14x + 30y s.t. 2x+5y≤200 7x+15y ≥ 420 x ≤2y x, y ≥0 The following solution is an optimal solution: HINT: The only correct answer listed below might not be a corner point! x=0 and y=40 x=60 and y=0 x=15 and y=21 x=0 and y=0
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- Based on Babich (1992). Suppose that each week each of 300 families buys a gallon of orange juice from company A, B, or C. Let pA denote the probability that a gallon produced by company A is of unsatisfactory quality, and define pB and pC similarly for companies B and C. If the last gallon of juice purchased by a family is satisfactory, the next week they will purchase a gallon of juice from the same company. If the last gallon of juice purchased by a family is not satisfactory, the family will purchase a gallon from a competitor. Consider a week in which A families have purchased juice A, B families have purchased juice B, and C families have purchased juice C. Assume that families that switch brands during a period are allocated to the remaining brands in a manner that is proportional to the current market shares of the other brands. For example, if a customer switches from brand A, there is probability B/(B + C) that he will switch to brand B and probability C/(B + C) that he will switch to brand C. Suppose that the market is currently divided equally: 10,000 families for each of the three brands. a. After a year, what will the market share for each firm be? Assume pA = 0.10, pB = 0.15, and pC = 0.20. (Hint: You will need to use the RISKBINOMLAL function to see how many people switch from A and then use the RISKBENOMIAL function again to see how many switch from A to B and from A to C. However, if your model requires more RISKBINOMIAL functions than the number allowed in the academic version of @RISK, remember that you can instead use the BENOM.INV (or the old CRITBENOM) function to generate binomially distributed random numbers. This takes the form =BINOM.INV (ntrials, psuccess, RAND()).) b. Suppose a 1% increase in market share is worth 10,000 per week to company A. Company A believes that for a cost of 1 million per year it can cut the percentage of unsatisfactory juice cartons in half. Is this worthwhile? (Use the same values of pA, pB, and pC as in part a.)A survey was conducted to 12 first time voters on their preferred candidate. The results are: BBM, BBM, LR, IM, PL, PL, IM, IM, BBM, BBM, LR, LR. Which statement is true? The Borda score of PL is two points. BBM wins by plurality method. The Condorcet winner is IM. The modes are LR and IM Which of the following is a property of all linear programming problems? alternate courses of action to choose from minimization of some objectives a computer program usage of graphs in the solutionBelow is a table that shows the Freshmen Enrollment of the New Texas Elementary School during the 1a Semesters of the past ten (10) Academic Years (AY), AY 2013-2014 2014-2015 2015-2016 2016-02017 2017-2018 Freshmen Enrollees AY 200 220 235 270 315 4. For the Weighted Moving Averages model, use: a weight of 0.40 for the most recent data; a weight of 0.35 for the second most recent data; and a weight of 0.25 for the third most recent data. You are the Principal of New Texas Elementary School. You are interested to know the forecast of freshmen enrolment for the next academic year (AY2023-2024), in order to plan ahead the necessary resources: faculty, classroom, library holdings, physical facilities, student services, furniture and fixtures, etc.). These are the requirements: AT 2013-2014 1. Calculate the forecast using 5 forecasting techniques/methodologies/models namely: Naïve Model, Unweighted and Weighted Moving Averages, Exponential Smoothing, and Time-Series Regression. Follow and…
- Calculating outcomes as equally likely would BEST describe: O a. Maximax criterion O b. Laplace criterion O c. Regret criterion Od. Maximin criterion Determining the average payoff for each alternative and choosing the one with the BEST payoff is the approach called: ea, maximax O b. minimax regret O c. laplace Od maximin MGraph the feasible region for the system of inequalities. 5x+y< -3 x-y > 3An airline company has drawn up a new flight schedule involving five flights. To assist in allocating five pilots to the flights, it has asked them to state their preference scores by giving each flight a number out of 10. The higher the number, the greater is the preference. Certain of these flights are unsuitable to some pilots owing to domestic reasons. These have been marked with a -. Flight Number Pilot I II III IV V A 8 2 - 5 4 B 10 9 2 8 4 C 5 4 9 6 - D 3 6 2 8 7 E 5 6 10 4 3 What should be the allocation of the pilots to flights in order to meet as many preferences as possible?
- Use the information below to answer question 2x + 3y + 3z = 2 4x – 3y – 6z = 2 10x – 6y + 3z = 0 1. Given values – 144, -192, and 96 for Dx, Dy, and Dz respectively and D = 144. Then the solution to the system for x, y and z are: A. -1, -1.33, and 0.67 B. -0.47, -0.63 and 0,30 C. 0.5, 0.67 and-0.33 D. 0.73, 0.98 and -0.49The following payoff table shows a profit for a decision analysis problem with two decision alternatives and three states of nature. In order to get full credit, show your all work done step by step including cell calculations using excel functions. State of Nature Decion Alternatives s1 s2 s3 d1 250 100 50 d2 100 75 100 a) Construct a decision tree for this problem. b) Suppose that the decision-maker obtains the probabilities P(s1)=0.65, P(s2)=0.15, and P(s3)=0.20. Use the expected value approach to determine the optimal decision.A farmer is considering planting five possible crop mixes. The outcomes depend on the weather (dry, average, or rainy). Assume the three possible weather states have probabilities: dry = 30%, average = 40%, rainy = 30%. Answer the following two questions. Mix A Mix B Mix C Mix D Mix E Dry -1 1 -1 2 01 5 Avera ប្តី ge T 1 -1 5 2 3 Rainy 9 54 13₂ 2
- The management is faced with the problem of choosing one of the products for manufacturing. The probability matrix after market research for the two products was as follows: State of nature Acts Good Fair Poor Product 'A' 0.75 0.15 0.10 Product 'B' 0.60 0.30 0.10 The profits that the management can make for different levels of market acceptability of the products are as follows : Profit (in Rs.) if market is Acts Good Fair Poor 35,000 15,000 5,000 Product 'A' Product 'B' 50,000 20,000 Loss 3,000 Calculate expected value of the choice of alternative and advise the management.The following payoff table shows the profit for a decision problem with two states of nature and two decision alternatives. Decision Alternative State of Nature 51 d₂ d2 (a) Use graphical sensitivity analysis to determine the range of probabilities of state of nature s, for which each of the decision alternatives has the largest expected value. d: is optimal for p(s₂) ≤ 0.2857 ; d. ✓ is optimal for p(s₂) > 0.2857 12 52 6 3 5 (b) Suppose P(s) = 0.2 and P(5₂) = 0.8. What is the best decision using the expected value approach? The best decision is d: with an expected value of 5.2 (c) Perform sensitivity analysis on the payoffs for decision alternative d₁. Assume the probabilities are as given in part (b), and find the range of payoffs under states of natures, and s₂ that will keep the solution found in part (b) optimal. As long as the payoff for s, is --?-- , then d₂ will be optimal. As long as the payoff for s₂ is --?-- Is the solution more sensitive to the payoff under state of nature…A firm that plans to expand its product line must decide whether to build a small or a large facilityto produce the new products. If it builds a small facility and demand is low, the net present valueafter deducting for building costs will be $400,000. If demand is high, the firm can either maintainthe small facility or expand it. Expansion would have a net present value of $450,000, and maintaining the small facility would have a net present value of $50,000.If a large facility is built and demand is high, the estimated net present value is $800,000. If demandturns out to be low, the net present value will be – $10,000.The probability that demand will be high is estimated to be .60, and the probability of low demandis estimated to be .40. 1- Compute the EVPI 2- Determine the range over which each alternative would be best in terms of the value of P ( low demand )