Maxima question (1 Viewer)

[Aysce]

Hello! I am new to this but Q: The sum of the dimensions of a box with a square base is 60cm. Find the dimensions that will give the box a maximum volume. Thanks in advance

 

[bleakarcher]

Let the box have square base of side length x cm and height y cm.
2x+y=60=>y=60-2x
V=x^2*y
Hence, V(x)=x^2[60-2x]=60x^2-2x^3
V '(x)=120x-6x^2
Max. volume V occurs when V '(x)=0,
=>120x-6x^2=6x[20-x]=0
:.x=0,20
But V(0)=0, hence max. volume occurs when x=20.
y=60-2(20)=20
Hence, max. volume occurs when the box has dimensions 20cm by 20cm in the base and height 20cm.

 

[Aysce]

Ohh damn thanks, should've read the question more times. Cheers buddy ^^

 

[bleakarcher]

any time dude