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Colorado Technical University MATH 451 Math 451 What is the probability of having a negative response (NS) for the high demand (HD)? P(NS|HD) = 0.16 P(NS|HD) = 0.875 P(NS|HD) = 0.40 P(NS|HD) = 84% Solution ...

Colorado Technical University MATH 451 Math 451 What is the probability of having a negative response (NS) for the high demand (HD)? P(NS|HD) = 0.16 P(NS|HD) = 0.875 P(NS|HD) = 0.40 P(NS|HD) = 84% Solution What is the probability of having a positive response (PS)? P(PS) = 47.10% P(PS) = 0.5290 P(PS) = 0 P(PS) = 1 Solution What is the revised probability of having the low demand (LD) for a positive response (PS)? P(LD|PS) = 0.1588 P(LD|PS) = 12.5% P(LD|PS) = 0.7940 P(LD|PS) = 5.66% Suppose that your friend has a loaded coin that comes up heads 70% of the time and another coin that looks just like the weighted one but is fair. Your friend pulls a coin at random out of his pocket and offers you a bet where he gets $1 if the heads side appears. How much must you get for a tail for this bet to be fair? $0.90 $1.60 $1.00 $1.50 Solution Your friend lets you test the coin by flipping it once, and it comes up heads. Given this new information, what is the probability that you have coin A (i.e., the one loaded for heads)? 0.467 0.529 0.333 0.500 What is the range of utility function in the utility theory? 0 ≤ utility function ≤ 1 -1 ≤ utility function ≤ 1 Utility function ≤ 1 Utility function ≥ 0 What is risk premium? (Expected monetary value (EMV)) - (Certainty equivalent) (Certainty equivalent) * (Expected monetary value (EMV)) (Expected monetary value (EMV)) + (Certainty equivalent) (Certainty equivalent) - (Expected monetary value (EMV)) In formulas, a function f is concave if, for any Suppose that a utility function of monetary return is concave. What does that imply about the attitude toward risk? Risk-averse Risk-seeking Risk-averse where the function is increasing, risk-seeking where the function is decreasing Cannot say without more information about the function Which one of the following is incorrect regarding utility theory? A person’s utility function is always the same. A person’s utility function can change at different times. A person may have different utility functions for different magnitude of money. A person’s attitude toward money can change over the time. What value is assigned to the worst payoff in the utility theory? A negative number 0 A positive number 1 Which of the following cannot be Allen’s certainty equivalent value if Allen has a 30% chance of winning a contract for $100,000 and 70% chance of winning another contract for $250,000? $150,000 $15,000 $1 $250,001 Suppose that a utility function of monetary return is convex. What does that imply about the attitude toward risk? Risk-averse Risk-averse where the function is increasing, risk-seeking where the function is decreasing Risk-seeking Risk-averse where the function is decreasing, risk-seeking where the function is increasing What is the expected monetary value (EMV) if Allen has a 30% chance of winning a contract for $100,000 and 70% chance of winning another contract for $250,000? $205,000 $145,000 $350,000 $150,000 Using the bonus payment, what is the utility of getting $100 below the $1,300? What is the utility of achieving the $1,300? What about $1,400? 100, 0, 0 100, 50, 0 0, 0, 100 -50, 0, 50 Utility theory is one way of dealing with the fact that people often act in ways that defy the cramped vision of economists. Suppose that you prefer to take $20,000 over a bet that offers a 50% chance of winning $50,000 and a 50% chance of getting nothing. Are you risk-seeking, risk-averse, or risk-neutral? What is the risk premium? Risk-averse, >5,000 Risk-neutral, <5,000 Risk-seeking, >5,000 Risk-averse, <5,000 An increasing concave utility function implies which of the following? a. Loss avoidance, a loss is felt more strongly than an equal gain b. Increasing return to scale c. Law of diminishing returns d. Pareto principle that 80% of the effects comes from 20% of the causes e. The Peter principle that people rise to their level of incompetence A,C Who has a risk premium of 0.50? Risk averse person Risk indifferent person Risk seeker person Risk avoider person What is the value of risk premium for a risk prone person? Greater than 0 Less than 0 0 Undefined What is the value of risk premium for a risk avoider person? Greater than 0 Undefined 0 Less than 0 hat is the flow balance constraint for New York? XNM + XNR ≤ 200 $20XNM + $15XNR ≤ 200 $20XNM + $15XNR ≥ 200 XNM + XNR ≥ 200 uppose that there is an outbreak of a dangerous disease and that the capacity at Factory 3 is reduced to 237 units. Under these circumstances, how many units are shipped from Factory 2 to Warehouse 3? 408 13 369 0 How many chairs were shipped to Memphis from Kansas City? 200 400 0 850 Suppose that there is an outbreak of a dangerous disease and that the capacity at Factory 3 is reduced to 237 units. What is the total cost, rounded off to the nearest whole number? 3,053 17,389 237 9,632 Suppose that there is an outbreak of a dangerous disease and that the capacity at Factory 3 is reduced to 237 units. The disease has spread, and the manager of Factory 1 has decreed that no more than 150 units may be shipped to any of the warehouses. How many units are shipped from Warehouse 3 to Destination 1? 37 113 144 0 How many chairs were shipped from Charlotte? 850 150 200 250 What is the significance of the negative values associated to nodes D_1 through D_4? Does the actual flow have to be less than, less than or equal, equal to, greater than or equal, or greater than these values? Net flow out, equal Net flow out, greater than Net flow in, equal Net flow out, less than or equal What is the total cost? 4,273 9,326 9,599 10,139 What is the value of the objective function? $34,700 $33,700 $34.950 $0 How many chairs were shipped to Richmond from Charlotte? 250 0 100 200 Suppose that there is an outbreak of a dangerous disease and that the capacity at Factory 3 is reduced to 237 units. The disease has spread, and the manager of Factory 1 has decreed that no more than 150 units may be shipped to any of the warehouses. What is the total cost to ship? Round your answer off to the nearest dollar. $8,900 $9,873 $9,961 $9,762 Note that the cost numbers are in cells C20:L29. For example, cell C20 has 8.9, C21 has 9.76. The decision variables can be found in a corresponding portion of the spreadsheet, C6:L15. What is the objective function? =SUM(F6:H8)*SUM(F20:H22)+SUM(I9:L11)*SUM(I23,L25) =SUMPRODUCT(F6:H8,F20:H22)+SUMPRODUCT(I9:L11,I23:L25) =SUMPRODUCT(F6,H8,F20,H22,I9,L11,I23,L25) =SUMPRODUCT(F6,H8,F20,H22)+SUMPRODUCT(I9,L11,I23,L25) What is the flow balance constraint for Denver? $15XMD + $25XRD ≤ 100 XMD + XRD > 100 $15XMD + $25XRD < 100 XMD + XRD = 100 Which factories are idle? Factory 3 is idle. Factories 2 and 3 are idle. Factory 2 is idle. Factory 1 is idle. Which of the following is a transshipment node? Richmond Atlanta Houston Los Angeles What is the flow balance constraint for Richmond? ($15XRA + $20XRH + $25XRD + $30XRL) – ($15XNR + $23XKR + $25XCR) ≤ 0 ($15XRA + $20XRH + $25XRD + $30XRL) – ($15XNR + $23XKR + $25XCR) = 0 (XRA + XRH + XRD + XRL) - (XNR + XKR + XCR) = 0 (XRA + XRH + XRD + XRL) – (XNR + XKR + XCR) > 0