Problem 2 (Individual): Wastewater Problem

You manage a seaside resort complex consisting of 143 time-share condominiums. On any given day, each condominium unit in the complex has an 87% chance of being occupied, independent of all other units. Each occupied unit produces a random amount of wastewater with a mean of 22.3 gallons and a standard deviation of 19.2 gallons, independent of all the other condominiums units. Vacant units do not produce any wastewater.

You process the wastewater from condominiums in treatment devices, each of which leases for $33.40 per day and can process up to 500 gallons of water per day. You are considering leasing 4, 5, 6, or 7 treatment devices. If the condominiums produce more wastewater than you are able to process, you must pay the municipal government a pollution fee of 10.5 cents for each gallon you do not process.

Which number of treatment devices will give you the lowest daily cost?