A construction engineer is selecting the pavement material for the landing strip of a new airport....

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A construction engineer is selecting the pavement material for the landing strip of a new airport. There are two kinds of pavement materials available: namely, good quality material (G) that costs $0.4 million and regular quality material (R) costing $0.28 million. Both of these materials will last for 10 years with proper maintenance. The maintenance cost will depend on the quality of the pavement material as well as the volume of traffic, as follows: a) b) c) The project planners estimate that there is 30% probability that in the next 10 years the air traffic volume will be high. Material Quality Good (G) Good (G) Regular (R) Regular (R) P(A/B) Without any additional information and assuming expected monetary value (EMV) criterion, which pavement material should the construction engineer select? = A research group is willing to conduct a study to predict the traffic volume for a price of $20,000. However, the prediction from this research group is not perfectly reliable. If the future true state of traffic is High (T), the group will predict High (S) with probability 0.9 and Low (S) with probability 0.1. In other words P(S1|T) = 0.9 and P(S2| T) = 0.1. Similarly, P(S2/T2) = 0.9 and P(S| T2) = 0.1. Where S and S2 represent predicting High and Low traffic, respectively, and T and T2 represent true state of High and Low traffic, respectively. Should such a study be performed before the selection of the pavement material? Traffic High Low What is the value of information of this study? P(B|A). P(A) P(B) n High Low Maintenance Cost Over 10 years $0.2 million $0.1 million $0.4 million $0.2 million P(A) = P(A/B).P(B) i=1 A construction engineer is selecting the pavement material for the landing strip of a new airport. There are two kinds of pavement materials available: namely, good quality material (G) that costs $0.4 million and regular quality material (R) costing $0.28 million. Both of these materials will last for 10 years with proper maintenance. The maintenance cost will depend on the quality of the pavement material as well as the volume of traffic, as follows: a) b) c) The project planners estimate that there is 30% probability that in the next 10 years the air traffic volume will be high. Material Quality Good (G) Good (G) Regular (R) Regular (R) P(A/B) Without any additional information and assuming expected monetary value (EMV) criterion, which pavement material should the construction engineer select? = A research group is willing to conduct a study to predict the traffic volume for a price of $20,000. However, the prediction from this research group is not perfectly reliable. If the future true state of traffic is High (T), the group will predict High (S) with probability 0.9 and Low (S) with probability 0.1. In other words P(S1|T) = 0.9 and P(S2| T) = 0.1. Similarly, P(S2/T2) = 0.9 and P(S| T2) = 0.1. Where S and S2 represent predicting High and Low traffic, respectively, and T and T2 represent true state of High and Low traffic, respectively. Should such a study be performed before the selection of the pavement material? Traffic High Low What is the value of information of this study? P(B|A). P(A) P(B) n High Low Maintenance Cost Over 10 years $0.2 million $0.1 million $0.4 million $0.2 million P(A) = P(A/B).P(B) i=1