A bulk belt conveyor is to be used to convey grain horizontally over a distance of 150. The grain weighs 50 lb/ft3. It is required that the conveyor deliver grain at a rate of 250 tph. The available belt widths are 18, 24, 30, and 36.

a. Determine the belt width and speed that delivers exactly the required capacity at the lowest horsepower to drive the empty conveyor.

b. Suppose the cost of the 150 conveyor is a function of the belt width and horsepower;

specifically, suppose it costs $300 per inch of belt width and $5,000 per increment of horsepower. Determine the belt width that yields the least-cost combination of belt width and horsepower.