A facility has a waste storage tank with a capacity of 40 cubic feet. Each week...

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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 tankâ€™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

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Since each week the tank produces either 0 10 20 or 30 cubicfeet of waste with respective probabilities of 01 04 03 and02 and the the contract service comes at the end of the week andremoves all of the waste in the tank if it exceeds 20 cubic fetthe amount of waste in the tank at the end of the week can be 010 20 cubic feet at the end of the week We can model the amountof waste in the tank at the end of the week as a Markov chain with3 states S0 S10 S20 denoting the amount of waste in the See Answer

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