A facility has a waste storage tank with a capacity of 40 cubicfeet. Each week the tank produces either 0, 10, 20, or 30 cubicfeet of waste with respective probabilities of 0.1, 0.4, 0.3, and0.2. If the amount of waste produced in a week creates a situationwhere the tank would overflow, the amount exceeding the tank’scapacity can be removed at a cost of $3 per cubic foot. At the endof each week, a contracted service is available to remove waste.The service costs $40 for each visit plus $1 per cubic foot ofwaste removed. The facility manager decides to adopt a policywhere, if the tank contains more than 20 cubic feet of waste, thecontract service comes at the end of the week and removes all ofthe waste in the tank. Otherwise, the service does not come, and nowaste is removed. Model the amount of waste in the tank as a Markovchain. Pay particular attention to when (at what point in the week)the amount of waste is measured or recorded
