In order to provide drinking water as part of its $50-$year plan, a west coast city is considering constructing a pipeline for importing water from a nearby community that has a plentiful supply of brackish ground water. A full$-$sized pipeline can be constructed at a cost of $$100\mathrm{.}0$ million now. Alternatively, a smaller pipeline can be constructed now for $$60\mathrm{.}0$ million and enlarged $15\mathrm{.}00$ years from now for another $$105\mathrm{.}0$ million. The pumping cost will be $$25,000$ per year higher for the smaller pipeline during the first $15\mathrm{.}00$ years, but it will be approximately the same thereafter. Both pipelines are expected to have the same useful life with no salvage value.