Problem 1: Wastewater Problem You are managing a seaside resort complex consisting of 145 time-share condominiums. On any given day, each condominium unit in the complex has an 85% 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 $32.50 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? Use @Risk simulation to answer the above question. Use a sample size of 1000 for each scenario. Problem 2: Maintenance Shop Operation You operate a maintenance shop that repairs aircraft engine compressors for a large airline. The number of compressors you receive to be repaired each day is Poisson with a mean value of 8.1. The crucial step in each repair operation is realigning the compressor's blades. The machine has a part that wears out rapidly, as follows: Days of Use Chance of Part Failure 1 2% 2 4% 3 8% 4 12% 5 18% 6 24% 7 or higher 32% On days when the part does not fail, you can process 10 compressors. On days when it does fail, you are equally likely to be able to process 0, l, 2, 3, 4, 5, 6, 7, 8, or 9 compressors. After a failure, you must replace the part and wait until the next day to resume work. On any given day, if you have more compressors to repair than you are able to x, you set the leftover compressors aside in a queue, and try to x them the next day. You estimate that each day each compressor waits in this queue costs you $80. Your policy is to replace the alignment machine part after in days of use or when it fails, whichever comes rst. You perform the replacement just before the start of each day's work. Replacement costs $500, whether done intentionally, or because of failure. (Occasionally, you will have to replace a part twice in one day: intentionally at the start of the day, and then later in the day because of a part failure.)