If the embankment should be built and if yes, to which of the five heights above the roadway should it be built.
Answer to Problem 30P
Yes, the embankment can be built.
The lowest total expected annual cost is at
Explanation of Solution
Given:
The
Concept used:
Write the expression for the annual probability of flood damage.
Here, the annual probability of flood damage is
Write the expression for the expected annual damage cost.
Here, the expected annual damage cost is
Write the expression for the factor
Here, the rate of interest is
Write the expression for the equivalent uniform annual cost for the embankment.
Here, the initial cost is
Write the expression for the total expected Annual cost.
Here, the total expected Annual cost is
Calculation:
Calculate the annual probability of flood damage and the expected annual damage cost.
Embankment height above roadway |
Initial cost |
Average frequency that will exceed height |
Annual probability of flood damages |
Expected annual damage cost |
Here, calculate the annual probability of flood damage and the expected annual damage cost from Equation-(I) and Equation-(II).
Calculate the factor
Substitute
Calculate the equivalent uniform annual cost for the embankment and total expected annual cost.
Embankment height above roadway |
Initial cost |
Expected annual damage cost |
Total Expected Annual cost |
||
Here, calculate the equivalent uniform annual cost for the embankment and total expected annual cost from Equation-(IV) and Equation-(V) respectively.
The lowest total expected annual cost is at
Conclusion:
Yes, the embankment can be built.
Thus, the lowest total expected annual cost is at
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Chapter 10 Solutions
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