Optimaztion

[jon12]

A rectangle is constructed with one side on the positive x-axis, one side on the positive y-axis, and the vetex opposite the origin on the line y=10-2x. What are the dimension of the rectangle of maximum area, and what is the area?
Optimization problems are quite difficult. The biggest problem I have is with setting these kinds of problems up. If anyone can help, I really appreciate it.

 

[galactus]

The area of the rectangle is A=xy

But, you know what y is?. It's y=-2x+10

Sub it in:

\(\displaystyle A=x(-2x+10)\)

Now, optimize.

 

[jon12]

Galactus can you provide me with any additional help on this problem/

 

[Jaskaran]

Foil it out, so it becomes A(x) = -2x^2 + 10x

Now, solve for 0, so 0<x<10 (0 or 10)

Take d/dx of A(x) = -4x + 10 = 0 = 2.5

Do u know how to optimize?

 

[Deleted member 4993]

A rectangle is constructed with one side on the positive x-axis, one side on the positive y-axis, and the vetex opposite the origin on the line y=10-2x. What are the dimension of the rectangle of maximum area, and what is the area?
Optimization problems are quite difficult. The biggest problem I have is with setting these kinds of problems up. If anyone can help, I really appreciate it.

Jon,

You have posted several problems - without showing a line of work for it.

Are these problems from take-home test?