Answer:
The minimum cost of installing the cable is $156.
Step-by-step explanation:
We have an optimization problem.
We have to minimize the cost of the cable.
We will use the variable x to express the the length of cable CP and PM, accordingly to the attache picture.
The length of the cable that goes from C to P (let's call it CP) is x.
Then, the length of the cable that goes from P to M (PM) can be calcualted usign the Pithagorean theorem:
The cost function Y is:
To optimize this cost funtion we have to derive and equal to 0:
The valid solution is x=21, as x can not phisically larger than 33.
The cost then becomes:
