SOLUTION: We're doing maximums and minimums of functions in my precalc class and i'm just not sure what to do with this word problem. If you could please give it a look and get back to me.

Click here to see ALL problems on Miscellaneous Word Problems

Question 644640: We're doing maximums and minimums of functions in my precalc class and i'm just not sure what to do with this word problem. If you could please give it a look and get back to me.
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.
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
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
the graph

Ti83 gave a minimum cost of $3,118 when x = 55.3 meters