"An aircraft control actuator is part of the flight control system that enables an airplane to fly. It is important that the actuators are reliable. Reliability can be defined as the probability a system is functioning, so it is a number between 0 and 1. The development and installation cost as a function of reliability equals [$1680+ $14227*(In R)], which will be paid immediately. Maintenance on the actuator will occur in year 4 and in year 9. In each year the maintenance cost as a function of reliability R is [$1500/ln(1.45R)]. These equations are only valid for reliability R > 0.7. Assume the interest rate is 12%.

What is the optimal reliability (a decimal between 0.7 and 1, rounded to the nearest hundreth) of the actuator that minimizes the discounted lifecycle costs of the actuator? (You do not need to calculate annual equivalent cost, but you do need to calculate the present value of the costs.)"