Question 644640
Suppose that the cost of laying cable on land is $20 per meter and the
 cost of laying cable under water is $30 per meter.
 In the diagram below the river is 50 meters wide and the distance AC
 is 100 meters.
 Express the cost of laying cable from A to B as a function of the distance
 from A to P.
 Use a graphing utility to find the location of P that minimizes the cost
 of laying the cable from A to B.
I'm not really sure how to do any of this. I figure that the distance a to p is 100-x but i'm not sure where to go from there. 
:
If I understand this correctly? 
  x = dist from A to P and,
 (100-x) = dist from P to c which is directly across form B
  The cable under water will be from P to B
:
Total Cost = Land cost + water cost
C(x) = 20x + 30{{{sqrt((100-x)^2 + 50^2)}}}
the graph
{{{ graph( 300, 200, -50, 150, -1000, 5000, 20x+30*sqrt((100-x)^2+50^2)) }}}
Ti83 gave a minimum cost of $3,118 when x = 55.3 meters