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Answer:
Cost of material is $245.31
Step-by-step explanation:
Let dimension of box,
- Length, l = x m
- Width, w = y m
- Height, h = z m
<em>The length of this base is twice the width.</em>
<em>∴ </em>x = 2y
Volume of box = 10 m³
∴ xyz = 10
⇒ 2y²z = 10
⇒ y²z = 5
<em>Material for the base costs $15 per square meter.</em>
Total cost of base = 15xy
Total cost of base = 30y² [∵ x = 2y ]
<em>Material for the sides costs $9 per square meter.</em>
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