One of the industrial robots designed by a leading producer of servomechanisms has four major components. components’ reliabilities are .98, .95, .94, and .90. all of the components must function in order for the robot to operate effectively. designers want to improve the reliability by adding a backup component. due to space limitations, only one backup can be added. the backup for any component will have the same reliability as the unit for which it is the backup. what will be the highest reliability the robot can achieve?

An external consultant recommends that a plant installs a bank of capacitors for power factor correction. this will reduce the peak electrical demand charges by an average of 93 kw every month. the plant current pays $13 per kw in peak demand charges. the capacitor bank will include 223 kw of fixed capacitors, and 183 of variable capacitors. the fixed capacitors cost $59 per kw, and the variable capacitors will cost $65 per kw. the consultant charges 21% of the equipment costs to install the capacitors. because this project will reduce the demand for the electric utility, they are prepared to provide a one-time rebate of $42 per kw of reduced demand. what is the simple payback period for this project (in years)?