An elevator, having a weight of 500 lb, needs to be lifted a distance y = 20ft, starting from rest and then stopping after at t=6 sec. A single motor and cable-winding can be mounted anywhere and used for the operation. During any lift or decent the acceleration should not exceed 10 ft/s^2. Design a cable-and-pulley system for the elevator, and estimate the material cost if the cable is $1.30/ft and pulleys are $3.50 each. Submit a drawing, include plots for the power output required of the motor and the elevator's speed versus the height y traveled.