Fred has bought a piece of land and intends to build his house on that land. The first thing he needs to do is to drill a well for drinking water. The depth of the aquifer (underground water table) in that part of the country varies between 20 to 100 meters and Fred doesn't know if he can get to it using the local drilling truck (LDT) that can reach down to 30 meters depth but no deeper. The alternative is to call a major drilling company (MDC) whose drilling equipment will reach the aquifer at any depth. If there is water on the property at less than 30 meters then for each hole drilled by the LDT there is a 50% chance of reaching water. Each hole will cost $500 whether water is found or not. The MDC, on the other hand charges a flat rate of $3000 to drill a well and the results are guaranteed. Based on information he got before buying the land, Fred believes that with probability P there is water on his property at less than 30 meters depth. His objective is to have the well done at least cost. The LDT owner told Fred that because of prior commitments he will be able to drill two holes at most on Fred's property but Fred must decide right away if and for how many holes he wants to hire him. So Fred has three options: 1) Calling immediately the MDC 2) Hire the LDT to drill one hole and if no water is found then call the MDC 3) Hire the LDT to drill two holes and if no water is found call the MDC (The LDT contract specifies that if it is hired for two holes but water is found on the first hole then Fred has the option of canceling the second drilling (which is no longer needed) and getting a $250 refund.) a- Draw a decision tree describing Fred's decision problem. b- Suppose that the MDC cost is K (rather than $3000). Obtain an expression for P as a function of K for which Fred will be indifferent between calling MDC immediately (alternative 1) vs. hiring LDT for one hole (Alternative 2)
Fred has bought a piece of land and intends to build his house on that land. The first thing he needs to do is to drill a well for drinking water. The depth of the aquifer (underground water table) in that part of the country varies between 20 to 100 meters and Fred doesn't know if he can get to it using the local drilling truck (LDT) that can reach down to 30 meters depth but no deeper. The alternative is to call a major drilling company (MDC) whose drilling equipment will reach the aquifer at any depth. If there is water on the property at less than 30 meters then for each hole drilled by the LDT there is a 50% chance of reaching water. Each hole will cost $500 whether water is found or not. The MDC, on the other hand charges a flat rate of $3000 to drill a well and the results are guaranteed. Based on information he got before buying the land, Fred believes that with probability P there is water on his property at less than 30 meters depth. His objective is to have the well done at least cost. The LDT owner told Fred that because of prior commitments he will be able to drill two holes at most on Fred's property but Fred must decide right away if and for how many holes he wants to hire him. So Fred has three options: 1) Calling immediately the MDC 2) Hire the LDT to drill one hole and if no water is found then call the MDC 3) Hire the LDT to drill two holes and if no water is found call the MDC (The LDT contract specifies that if it is hired for two holes but water is found on the first hole then Fred has the option of canceling the second drilling (which is no longer needed) and getting a $250 refund.) a- Draw a decision tree describing Fred's decision problem. b- Suppose that the MDC cost is K (rather than $3000). Obtain an expression for P as a function of K for which Fred will be indifferent between calling MDC immediately (alternative 1) vs. hiring LDT for one hole (Alternative 2)
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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PLEASE SOLVE USİNG DECİSİON ANALYSIS
Transcribed Image Text:Fred has bought a piece of land and intends to build his house on that land. The first thing he
needs to do is to drill a well for drinking water. The depth of the aquifer (underground water
table) in that part of the country varies between 20 to 100 meters and Fred doesn't know if
he can get to it using the local drilling truck (LDT) that can reach down to 30 meters depth
but no deeper. The alternative is to call a major drilling company (MDC) whose drilling
equipment will reach the aquifer at any depth. If there is water on the property at less than
30 meters then for each hole drilled by the LDT there is a 50% chance of reaching water.
Each hole will cost $500 whether water is found or not. The MDC, on the other hand
charges a flat rate of $3000 to drill a well and the results are guaranteed. Based on
information he got before buying the land, Fred believes that with probability P there is
water on his property at less than 30 meters depth. His objective is to have the well done at
least cost. The LDT owner told Fred that because of prior commitments he will be able to
drill two holes at most on Fred's property but Fred must decide right away if and for how
many holes he wants to hire him. So Fred has three options:
1) Calling immediately the MDC
2) Hire the LDT to drill one hole and if no water is found then call the MDC
3) Hire the LDT to drill two holes and if no water is found call the MDC
(The LDT contract specifies that if it is hired for two holes but water is found on the first hole
then Fred has the option of canceling the second drilling (which is no longer needed) and
getting a $250 refund.)
a- Draw a decision tree describing Freď's decision problem.
b- Suppose that the MDC cost is K (rather than $3000). Obtain an expression for P as a
function of K for which Fred will be indifferent between calling MDC immediately
(alternative 1) vs. hiring LDT for one hole (Alternative 2)
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