Question

Would the answer be 2000 to this? with 1,200 i got 4,000?

If 600cm^2 of material is available to make a box with a square base and a closed top, find the maximum volume of the box in cubic centimeters.

Answer 1

2x^2 + 4xy = 600
4xy = 600 -2x^2
y = (300 -x^2)/2x

v = x^2y
= x^2(300-x^2)/2x
= 150x - x^3/2
dv/dx = 150 - 3/2 x^2
0 = 150 -3/2 x^2
x = 10

y = (300 - 10^2 )/2*10
y = 10
V = x^2 y
V = 10^2 (10)
V= 1000 Cm^2