A trapezoidal channel is to be designed to carry a discharge of 250 cfs at a normal depth of 3.5 ft. The channel is running on a slope of 0.005 ft/ft and the side slopes can be no steeper than 2.5 H on 1 V. The channel is earthen and will have an estimated Manning n value of 0.03. What is the minimum bottom width to effect the required normal depth?