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Let x be the distance from C to P.
The cost of installing the cable is 3x + 5(16 - x) = 3x + 80 - 5x = 80 + -2x
To minimize the cost, we need to find the value of x that minimizes the cost.
Taking the derivative of the cost function with respect to x, we get -2. Setting this equal to 0 and solving for x, we get x = 40.
Therefore, the distance from C to P is 40 meters and the cost of installing the cable is minimized to $80.
A cable runs along the wall from C to P at a cost of $3 per meter, and straight from P to M at a cost of $5 per meter. If M is 16 meters from the nearest point A on the wall where P lies, and A is 50 mters from C, find the distance from C to P such that the cost of installing the cable is minimized and find this cost
1 answer
1 answer