The bathtub theory of operations management is being promoted as the next breakthrough for global competitiveness. The factory is a bathtub with 50 gallons of capacity. The drain is the outlet to the market and can output three gallons per hour when wide open. The faucet is the raw material input and can let material in at a rate of four gallons per hour. Now, to test your comprehension of the intricacies of operations (assume the bathtub is empty to begin with):

a. Draw a diagram of the factory and determine the maximum rate at which the market can be served if all valves are set to maximum. What happens to the system over time?

b. Suppose that instead of a faucet, a five-gallon container is used for filling the bathtub (assume a full container is next to the tub to begin with); it takes two hours to refill the container and return it to the bathtub. What happens to the system over time?