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A rectangluar open topped aquarium is to have a square base and volume 8m^3. The material for the base cost $1 per m^2, and the material for the sides cost $4 per m^2. What demensions minimize the cost of the aquarium?? 

 Apr 4, 2016

Best Answer 

 #2
avatar+95 
+5

Have you done the one where it is asking to find the max area of a right triangle?

 Apr 4, 2016
 #1
avatar+95 
+5

V=x^2y = 8 => 8/x^2

C= 1*x^2+4(4xy)

C= x^2+16xy

 

C(x)= x^2+16x* 8/x^2

C(x)= x^2+128/x

 

C'(x)= 2x-128/x = 0

2x = 128/x^2

2x^3=128

x^3=64

x=4

 

C''(x)= 2+256/x^3 >0, for all x>0

By the second derivative test for absolute min, cost is minimum when x=4, y= 1/2

 Apr 4, 2016
 #2
avatar+95 
+5
Best Answer

Have you done the one where it is asking to find the max area of a right triangle?

napoleonpp Apr 4, 2016
 #3
avatar+270 
+5

Yes, got 1/4m^2. You??

gretzu  Apr 4, 2016
 #4
avatar+95 
0

Ok good that's what I got haha 

 Apr 4, 2016
 #5
avatar+270 
0

Good, haha, i'm not as concerned about it now :P

gretzu  Apr 4, 2016

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