The bathtub theory of operations management is being promoted as the next breakthrough for global competitiveness. The factory is an open tank with 200 gallons of capacity. The drain is the outlet to the market and can output 50 gallons per hour when wide open. The faucet is the raw material input and can let material in at a rate of 60 gallons per hour. Now, to test your comprehension of the intricacies of operations (assume the tank 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. describe in words how the number of gallons in the open tank is changing over time and draw a graph of the situation (gallons in the open tank over time).