THout and TCout are not given.
Clearly, if THout is made equal to THin, no heat is extracted from the warm water, and the power output is zero. On the other hand, if THout is made equal to TCin, maximum power is extracted from the warm water but the output power is again zero because (as you are going to find out) the Carnot efficiency goes to zero.
Between these extremes, there must be a value of THout that maximizes power output. Determine this value, and determine the value of THout that maximizes the Carnot efficiency.
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