A rectangular storage container with an open top is to have a volume of 10 m3. The length of this base is twice the width. Material for the base costs $20 per square meter. Material for the sides costs $12 per square meter. Find the cost of materials for the cheapest such container.

Volume is defined as the space occupied by any object in the three-Dimensions. All three parameters are required for the volume like length, width, and height of cube or cubes.

The cost will be calculated as follows:-

V = 10 cubic meter
The length of this base is twice the width
Material for the base costs $20 per square meter
Material for the sides costs $12 per square meter

Area = w x 2w = 2w²

10 = w x 2w x H

H = w² / 5

Now the surface area will be calculated as:-

A = Base + ( 2 Side₁+ 2 Side₂)

Now the cost will be given as:-

C = 20 Base + 12 [ 2 Side₁ + 2Side₂ ]

C = ( 20 x LW ) + 12[ 2WH +4WH]

C = ( 20 x 2W²) +12[ 40W² +72 WH]

C = 40 W² + 72 x 5 / W²

C = 40W² + ( 360 / W)

Now differentiate the above equation and equate it with zero.

80W - ( 360 / W² ) = 0

( 360 / W² ) = 80W

W³ = ( 360 / 80 )

W = 1.65

C = 40W² +( 360/W )

C = 40( 1.65²) + ( 360/1.65)

C = 108.9 + 218. 18

C = $ 327.08

Therefore the cost of materials will be equal to $327.08

To know more about Volume follow

https://brainly.com/question/1972490

#SPJ1