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2 August, 02:57

A storage shed is to be built in the shape of a box with a square base. It is to have a volume of 250 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.

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  1. 2 August, 03:11
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    the dimensions of the most economical shed are height = 10 ft and side 5 ft

    Step-by-step explanation:

    Given data

    volume = 250 cubic feet

    base costs = $4 per square foot

    material for the roof costs = $6 per square foot

    material for the sides costs = $2.50 per square foot

    to find out

    the dimensions of the most economical shed

    solution

    let us consider length of side x and height is h

    so we can say x²h = 250

    and h = 250 / x²

    now cost of material = cost of base + cost top + cost 4 side

    cost = x² (4) + x² (6) + 4xh (2.5)

    cost = 10 x² + 10xh

    put here h = 250 / x²

    cost = 10 x² + 10x (250 / x²)

    cost = 10 x² + (2500 / x)

    differentiate and we get

    c' = 20 x - 2500 / x²

    put c' = 0 solve x

    20 x - 2500 / x² = 0

    x = 5

    so we say one side is 5 ft base

    and height is h = 250 / x²

    h = 250 / 5²

    height = 10 ft
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