For a half-gallon (1892.7 cubic cm) of milk, the bottom of the container costs three times as the sides, while the top of the container costs 5 times as much as the sides. Assuming a square base to a rectangular carton (i.e. don't worry about the oddly shaped top), find the dimensions that minimize the cost of the container. After you solve the problem, check how closely your findings match the actual dimensions of a half-gallon carton of milk.

Question

For a half-gallon (1892.7 cubic cm) of milk, the bottom of the container costs three times as the sides, while the top of the container costs 5 times as much as the sides.  Assuming a square base to a rectangular carton (i.e. don't worry about the oddly shaped top), find the dimensions that minimize the cost of the container.  After you solve the problem, check how closely your findings match the actual dimensions of a half-gallon carton of milk.

amistre64 · Answer

Volume = x^2(h)

1892.7 = x^2(h)

h = 1892.7/x^2

amistre64 · Answer

is it 5 times as much as all the sides combined?  or 5 times as much as 1 side?

anonymous · Answer

Cost = Top + Bottom + Sides
C = 5S + 3S + S

anonymous · Answer

C = 9S
S = xh
C = 9xh

C = (1892.9/x^2)(9x)