Minimizing Surface Area You want to design an open box (no lid) with a square base that has a volume of 5000 cubic inches. (a) Express the surface area S of the box as a function of x. (b) What must the height of the box be if each side of the square base is 10 inches?

Question

Minimizing Surface Area You want to design an open box (no lid) with a square base that has a volume of 5000 cubic inches.    (a)	Express the surface area S of the box as a function of x. (b)	What must the height of the box be if each side of the square base is 10 inches?

anonymous · Answer

min 2(x+y)z+xy=S
st: xyz=5000=V
so S=10000(x+y)/xy
S'x=0 and S'y=0
x=y, z=5000/x2
So S=20000/x
min S=20000/x when x=y=10
z=50