Model the amount of waste in the tank as markov chain

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Reference no: EM132295029

A facility has a waste storage tank with a capacity of 40 cubic feet. Each week the produces either 0, 10, 20, or 30 cubic feet of waste with respective probabilities of 0.1, 0.4, 0.3, and 0.2. If the amount of waste produced in a week creates a situation where the tank would overflow, the amount exceeding the tank’s capacity can be removed at a cost of $3 per cubic foot. At the end of each week, a contracted service is available to remove waste. The service costs $40 for each visit plus $1 per cubic foot of waste removed. The facility manager decides to adopt a policy where, if the tank contains more than 20 cubic feet of waste, the contract service comes at the end of the week and removes all of the waste in the tank. Otherwise, the service does not come, and no waste is removed.

(a) Model the amount of waste in the tank as a Markov chain. Pay particular attention to when (at what point in the week) the amount of waste is measured or recorded.

(b) Use your model to determine the average cost for waste removal the facility manager should budget per week over the long run.

Reference no: EM132295029

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