Solution) A drainage channel in a community where flash floods are experienced has a capacity sufficient to ca
Question: A drainage channel in a community where flash floods are experienced has a capacity sufficient to carry 700 cubic feet per second. Engineering studies produce the following data regarding the probability that a given water flow in any one year will be exceeded, and the cost or enlarging the channel to that water flow capacity.
| Water flow | Probability of greater flow | Capital investment to enlarge |
| (cu.ft.per second) | occurring in any one year | channel to carry this flow |
| 700 | 0.20 | None |
| 1,000 | 0.10 | $20,000 |
| 1,300 | 0.05 | $30,000 |
| 1,600 | 0.02 | $44,000 |
| 1,900 | 0.01 | $60,000 |
Record indicate that the average property damage amount to $20,000 when overflow occurs. It is believed that this would be that average damage whenever the storm flow is greater than the capacity of the channel.
Reconstruction/enlarging of the channel would be financed by 40 year bonds bearing 8% interest per year.
Should the channel be enlarged? If so, what is the most economical channel size in terms of having the lowest annual costs?
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