Mathematics: Astorage shed is to be built in the shape of a box with a square base. it is to have a volume of 1458 cubic feet. the concrete for the base costs $4 per square foot, the material for the roof costs $6 per square foot, and the material for the sides costs $2.50 per square foot. find the dimensions of the most economical shed.

Astorage shed is to be built in the shape of a

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30.12.2021

the length of base and height of shed are 9 cm and 18 cm respectively.

Step-by-step explanation:

let the length of the base be = x ft ( the base is square)

and height be = y ft

given volume o the shed = 1458 cm^3

⇒ x^2y= 1458

also, according to question total cost C

$C= 4x^2+6x^2+4xy\times2.5$

$C= 10x^{2}+ 10x\times y$

now put y= 1428/x^2 in the above equation

$C= 10 x^{2}+\frac{14580}{x}$

now differentiating we get

$C'= 20 x-\frac{14580}{x^{2}}$

now set it equal to zero for most economical cost

$20 x =\frac{14580}{x^{2}}$

on calculating we get x= 9 cm

and y= 18 cm

therefore, the length of base and height of shed are 9 cm and 18 cm respectively.

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