Design a rectangular milk carton box of width ww, length ll, and height hh which holds 474 cm3474 cm3 of milk. the sides of the box cost 2 cent/cm22 cent/cm2 and the top and bottom cost 3 cent/cm23 cent/cm2. find the dimensions of the box that minimize the total cost of materials used

L = W = 6.810 cm

H =  10.22 cm

Explanation:

given data

volume L W H = 474 cm³

sides of the box cost = 2 cent/cm²

top and bottom cost 3 cent/cm²

to find out

dimensions of the box that minimize the total cost of material use

solution

we know here L W H = 474

here L is length and B is width and H is height

so when we minimize the cost function

C( L, W, H ) = (2) 2 H ( L + W ) + (3) 2 L W

so put here H

substitute H =

we get

C( L, W ) = 1896 ( ) + 6 LW

so

minimum cost will be when the two partial derivatives is 0

so

= 6W - = 0

so  

= 6L - = 0

L =

so

by solving above equation we get

L = W = = 6.810 cm

and

H =

H =  10.22 cm

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the amount of current in the coil