Maximizing XY: Problem 2 Solution - No Numbers Given

[Econometricia]

1.http://www.teachingcenter.ufl.edu/materials/math_lab/oldtests/FA09_MAC2311_exam4ab.pdf Number 2



2. Maxamize XY subject to , y=sqrt(x)



3. I don't know what numbers to use...

 

[hotvette]

The first thing you need to do is determine what is to be maximized and write an equation for it. It's pretty clear from the sketch (and it isn't xy).

 

[Econometricia]

Maxamize Area. Area =(9-x)y

 

[hotvette]

OK, correct. These types of problems are single variable optimization problems. The expression you have for area has x and y. How would you express area in terms of x only?

 

[Econometricia]

OK so , A'= 9-3x
x=3
I plug X into A= (9-x)(sqrt(x))
So the Area is 6*sqrt(3).

 

[hotvette]

Correct.