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 $15 per square meter. Material for the sides costs $9 per square meter. Find the cost of materials for the cheapest such container. (Round your answer to the nearest cent.) $

Cost of material is $245.31

Step-by-step explanation:

Let dimension of box,

The length of this base is twice the width.

∴ x = 2y

Volume of box = 10 m³

∴ xyz = 10

⇒ 2y²z = 10

⇒ y²z = 5

Material for the base costs $15 per square meter.

Total cost of base = 15xy

Total cost of base = 30y²         [∵ x = 2y ]

Material for the sides costs $9 per square meter.

Total cost of side = 9(2xz+2zy)

Total cost of side = 18(xz+yz)

Total cost of material for container = 30y² + 18(xz+yz)

    [From (i)]

Differentiate w.r.t y

For critical point , C'(y)=0

The minimum cost of container material  at

Hence, the cheapest cost of material for container is $245.31

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step-by-step explanation: