The optimum design of a sewage-treatment plant involves minimizing the losses from possible over and under design. Altouney [1963] has reviewed 71 public-works population projections after a 15-year period. The mean ratio of actual to predicted population was found to be 0.88 and the standard deviation of the ratio was found to be 0.12, with the normal distribution providing a satisfactory fit.

Use the accompanying cost figures.† Assume that the population is estimated to be 100,000 in 15 years and waste generation is 100 gal/(capita)(day). Design is to be based only on conditions 15 years from now. Study alternate actions of design for 7, 8, 9, 10, 11, 12 million gal/day. Assume that the cost of adding capacity is $150,000 per million gal/day needed.