A flagship hotel in Cedar Falls must construct a retaining wall next to its parking lot due to the widening of the city's main thoroughfare located in front of the hotel. The amount of rainfall experienced in a short time may cause damage in varying amounts, and the wall increases in cost in order to protect against larger and faster rainfalls. The probabilities of a specific amount of rainfall in a 30-minute period and wall cost estimates are as follows:

The wall will be financed through a 6% per year loan. The principal and interest will be repaid over a 10-year period. Records indicate an average damage of $50,000 has occurred with heavy rains, due to the relatively poor cohesive properties of the soil along the thoroughfare. A discount rate of 6% per year is applicable. Find the amount of rainfall to protect against by choosing the retaining wall with the smallest AW value over the 10-yearperiod.

Rainfall, Inches Probability of First Cost of Wall, S 200,000 225,000 300,000 400,000 450,000 per 30 Minuts Greater Rai 2.0 2.25 2.5 3.0 3.25 0.3 0.05 0.01 0.005