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- [3c16]1/3,2[3c16]1/3 and [32c81]1/3.
- [9c16]1/3,2[9c16]1/3 and [32c81]1/3.
- [9c16]1/3,2[9c16]1/3 and [32c9]1/3.
- [81c16]1/3,2[81c16]1/3 and [32c81]1/3.

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Solution

Verified by Toppr

Let the breadth be x, length be 2x and height be h

V=x.2x.h

⇒c=2x2h ....(1)

Area of bottom =2x2 =Area of top

Area of sides =2xh+2xh+xh+xh=6xh.

If R rupees be the cost of material for bottom then for the top and sides is 3R.

∴E=R(2x2)+3R(2x2+6xh)

⇒E=R(8x2+18xh)

or E=R(8x2+18xc2x2)

⇒E=R(8x2+9cx)

where R and c are constants.

dEdx=R(16x−9cx2)

For maximum or minimum,

dEdx=0

∴x=(9c16)1/3

Also, d2Edx2=R(16+18cx3)=+ive

and hence minimum.

∴ dimensions are

[9c16]1/3,2[9c16]1/3 and [32c81]1/3.

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