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 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.

8 Figure 15 20 P A 24 M