Question

A group of class X students were asked to use steel rods, plastic ropes and jute
ropes to make the framework(i.e. edges) of a cuboid. They must use jute ropes
for the lengths, plastic ropes for the breadths and steel rods for the heights. If
the cost per unit length(Rs. per metre) of the jute ropes, plastic ropes and steel
rods are 1, 2 and 3 resp., and the volume of the cuboid should be exactly 36 cu.m,
what is the minimum cost( Rs.) of making the framework?​

Answer 1

Given : A group of class X students were asked to use steel rods, plastic ropes and jute ropes to make the framework(i.e. edges) of a cuboid.

cost per unit length(Rs. per metre) of the jute ropes, plastic ropes and steel rods are 1, 2 and 3 resp.

volume of the cuboid should be exactly 36 cu.m,

To Find : minimum cost( Rs.) of making the framework

Solution:

 Jute rope cost = Rs 1 /m

 plastic ropes  cost  = Rs 2 /m

 Steel rode  cost  = Rs 3 /m

we would like to have steel minimum

Assuming available in meters only

Volume = 36

= lbh

      S         P    J             cost

36  = 1   *  1  * 36        = 4( 3 * 1  + 2 * 1  +  1 * 36)    = 4(41)

36 =   1  *   2 * 18        = 4( 3 * 1  + 2 * 2  +  1 * 18)    = 4(25)

36 =   1  *   3 * 12       = 4( 3 * 1  +  2* 3  +  1 * 12)    =  4(21)

36 =   1  *   4 * 9        = 4( 3 * 1  +  2* 4  +  1 *9)    =     4(20)

36 =   1  *   6 *  6        = 4( 3 * 1  +  2* 6  +  1 *6)    =     4(21)

36 =  2  *   1 *  18        = 4( 3 * 2  +  2* 1  +  1 *18)    =     4(26)

36 =  2  *   2 *  9        = 4( 3 * 2  +  2* 2  +  1 *9)    =     4(19)

36 =  2  *   3 *  6        = 4( 3 * 2  +  2*3  +  1 *6)    =     4(18)

36 =  3  *   1 *  12        = 4( 3 * 3  +  2*1  +  1 *12)    =     4(23)

36 =  3  *  2 *  6        = 4( 3 * 3  +  2*2  +  1 *6)    =       4(22)

36 =  3  *  3 *  4        = 4( 3 * 3  +  2*3  +  1 *4)    =       4(19)

Minimum cost  of making the framework

36 =  2  *   3 *  6        = 4( 3 * 2  +  2*3  +  1 *6)    =     4(18)

jute ropes for the lengths   =        length = 6 m

plastic ropes for the breadths =>  breadth =   3m

steel rods for the heights  =>        height =  2  m

Minimum  Cost = 72  Rs

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