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A cable runs along the wall from C to P at a cost of ​$6 per​...

A cable runs along the wall from C to P at a cost of ​$6 per​ meter, and straight from P to M at a cost of ​$10 per meter. If M is 16 meters from the nearest point A on the wall where P​ lies, and A is 54 meters from​ C, find the distance from C to P such that the cost of installing the cable is minimized and find this cost.

The cost is minimized when the distance from C to P is _ meters.

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