# Thread: [SOLVED] applied optimization problem

1. ## [SOLVED] applied optimization problem

Two vertical poles, 10ft. apart, are both 10ft. tall. Find the length of the shortest rope that can reach from the top of one pole to a point between them, and then to the top of the other pole. To solve the problem, answer the following:

a) Express the length of rope used as a function of one variable.

b) Using the function you arrived at in part (a), determine the minimal length of rope needed. At what point on the ground will the rope touch?

2. Originally Posted by gator4life
Two vertical poles, 10ft. apart, are both 10ft. tall. Find the length of the shortest rope that can reach from the top of one pole to a point between them, and then to the top of the other pole. To solve the problem, answer the following:

a) Express the length of rope used as a function of one variable.

b) Using the function you arrived at in part (a), determine the minimal length of rope needed. At what point on the ground will the rope touch?
let $\displaystyle x$ = distance along the ground from the base of one pole to the point between

$\displaystyle 10 - x$ = distance from the same point to the other pole

length of the rope ...

$\displaystyle L = \sqrt{10^2 + x^2} + \sqrt{(10-x)^2 + 10^2}$

you do the optimization