Question

A cable runs along the wall from C to P at a cost of $8 per meter, and straight from P to M at a cost of $10 per meter. If M is 12 meters from the nearest point A on the wall where P lies, and A is 60 meters from C, find the distance from C to P such that the cost of installing the cable is minimized and find this cost .

Answer 1

To minimize the cost of installing the cable, the distance from C to P should be 0 meters, and the cost will be $120.

Step-by-step explanation:

To minimize the cost of installing the cable, we need to find the distance from C to P. Let's break down the problem step by step:

1. Let x be the distance from C to P.
2. The cost of running the cable from C to P is 8x.
3. The distance from P to M is 12 meters.
4. The cost of running the cable from P to M is 10 * 12 = 120 dollars.
5. The total cost of installing the cable is 8x + 120.

To minimize the cost, we need to minimize the expression 8x + 120. Since the cost per meter is the same for every meter of cable, the cost will be minimized when the distance from C to P is as short as possible. Therefore, the distance from C to P should be 0 meters, and the cost will be 120 dollars.