Reference no: EM133534668

Assignment:

A home-owner is building a house on the outskirts of a town and is considering the alternatives between drilling his own well on a one-acre property and subscribing to the city water. It cost $500 to drill a well and $200 to complete the necessary facilities if water is found in adequate quantity. The probability of striking a water-bearing stratum is estimated to be 0.4 in the vicinity. However, if the first well is dry, it may be assumed that any other well on the property will yield the same result. The city requires an immediate payment of $500 to make a connection. The present worth of water payments to the city is estimated at $1000 (if subscribe to the city water), whereas, the present worth of water operation and maintenance on a successful drilled well is only $300. Answer the following questions and draw the corresponding decision trees wherever appropriate.

(a) What should the engineer do if he is an EMV decision maker?

(b) An ultrasonic device to detect the presence of water can be rented. Although the device will indicate "wet" if there is a water-bearing stratum, it may fail to indicate "dry" in the absence of a water-bearing stratum. In this latter case, the device will read "wet" 30% of the time. How much should the engineer pay to rent the ultrasonic device to obtain additional information on the presence of water beneath his property?

(c) At most, how much should perfect information be worth (i.e., certain knowledge about whether or not a water-bearing stratum is present)?

(d) Suppose the probability of striking a water-bearing stratum in the vicinity can only be estimated within the range 0.3 to 0.5, Will the engineer still insist on his optimal decisions previously obtained in (a)? Justify.