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?
Answers
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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