Minimum surface

Find the length, breadth, and height of the cuboid-shaped box with a minimum surface area, into which 50 cuboid-shaped blocks, each with length, breadth, and height equal to 4 cm, 3 cm, and 2 cm respectively, can be packed.

Correct result:

x =  12 cm
y =  10 cm
z =  10 cm

Solution:

n=50 a=4 cm b=3 cm c=2 cm  V=n a b c=50 4 3 2=1200 cm3 1200=2×2×2×2×3×5×5=24×3×52  S=2 (xy+yz+xz)min  x1=V3=1200310.6266 cm  x=2 2 3=12 cm
y=5 2=10 cm
z=V/(x y)=1200/(12 10)=10 cm



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