calculus
posted by Angel .
A power station is on one side of a river that is 0.5 mile wide, and a factory is 5.00 miles downstream on the other side of the river. It costs $15 per foot to run overland power lines and $23 per foot to run underwater power lines. Estimate the value of x that minimizes the cost.
a. 1.00
b. 0.43
c. 0.00
d. 2.00
e. 1.44

The question did not define x, which is probably shown in a diagram.
Let us define x as the distance downstream of the power station across the river, to which point the underriver power line connects.
Then the cost function
C(x)=15*(5x)+23*sqrt(0.5^2+x^2)
You need to minimize C(x) with respect to x.
Can you take it from here? 
I will try but there is no diagram.

The solution for x does fit one of the answers. So the interpretation should be correct.
Respond to this Question
Similar Questions

11th Grademath
A power station and a factory are on opposite sides of a river 50 feet wide. A power line must be run from the station to the factory. It costs 25 dollars per foot to run the cable in the river and $15 per foot on land. Express the … 
calculus
A power station and a factory are on opposite sides of a river 50 feet wide. A power line must be run from the station to the factory. It costs 25 dollars per foot to run the cable in the river and $15 per foot on land. Express the … 
Math
Power Plant on the River Problem As the construction manager for the Lightem Up Power Company , you make decisions to hep minimize costs of the company's construction projects. Today you've been asked to determine the path of a pipe … 
math
A pottery factory needs to connect with the main gas pipe line. This pipeline is on the other side of a stream. A gas line must be run from the main line junction to the factory at the lowest possible cost. It costs $12.50 per foot … 
physics
Noah wants to swim across a river 10 m wide, flowing from north to south. He swims so his velocity with respect to the river is 2 m/s due east, and the river moves at 4 m/s. How far downstream in m from his starting point will he reach … 
physics
Noah wants to swim across a river 10 m wide, flowing from north to south. He swims so his velocity with respect to the river is 2 m/s due east, and the river moves at 4 m/s. How far downstream in m from his starting point will he reach … 
math
A power station is on one side of a river that is 3/4 mile wide, and a factory is 8 miles downstream on the other side of the river. It costs $24 per foot to run power lines over land and $30 per foot to run them under water.(1 mile … 
Calculus 1
a power station needs to supply power lines to a location 10 miles downstream and on the other side of a river that is 0.75 miles wide. Power lines cost $7 per foot on land and $10 per foot under water. What is the most economical … 
Calculus
A factory is located on one bank of a straight river that is 2000 m wide. On the opposite bank but 4500 m downstream is a power station from which the factory draws its electricity. Assume that it costs $3 per meter to lay an underwater … 
physics
A boat traveling at 116.5 m/s relative to the water aims to go straight across a river. If the river is 153 m wide and the current in the river is 3.50 m/s, how far downstream will the boat land on the other side of the river?