﻿ A box of constant volume C is to be twice as long as it is wide. The cost per unit area of the material on the top and four sides is three times the cost for bottom. What are the most economical dimensions of the box?   : Kaysons Education

# A Box Of Constant Volume C is To Be Twice As Long As It Is Wide. The Cost Per Unit Area Of The Material On The Top And Four Sides Is Three Times The Cost For Bottom. What Are The Most Economical Dimensions Of The Box?

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## Question

### Solution

Correct option is

Let 2x be the length, x be the width and y be the height of the box.

Volume = C = 2x2 y.

Let then cost of bottom = Rs. k per sqm.

Total cost = cost of bottom + cost of other faces

Eliminating y using C = 2x2y,

Total cost = 2k(4x2 + 9C/2x

Total cost is to be minimized

The dimensions are:

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