Chapter 2.5, Problem 27E

Cost A cable is to be installed from one corner, $C$, of a rectangular factory to a machine, $M$, on the floor. The cable will run along one edge of the floor from $C$ to a point, $P$, at a cost of $\$6$ per meter, and then from $P$ to $M$ in a straight line buried under the floor at a cost of $\$10$ per meter (see Fig. 15) Let $x$ denote the distance from $C\text{ to }P$. If $M$ is $24$ meters from the nearest point, $A$, on the edge of the floor on which $P$ lies, and $A$ is $20$ meters from $C$, find the value of $x$ that minimizes the cost of installing the cable and determine the minimum cost.