Question

A firm can produce three types of cloths A, B and C. Three kinds of wool are required
for it, say red, green and blue wool. One unit of type ‘A’ cloth needs 1 yard of red
wool, 2 yards of green and 3 yard of blue wool; one unit length of type ‘B’ cloth needs
2 yard of red, 3 yards of green and 4 yards of blue wool; one unit length of type ‘C’
cloth needs 3 yards red, 4 yards of green and one yard of blue wool. The firm has only
a stock of 14 yards red, 20 yards green and 14 yards of blue wool. If total stock is used,
then determine the number of units of cloth A, B and C, write the mathematical
formulation to the problem and solve it by using LU decomposition method.​

Answer 1

there is mistake in data

Step-by-step explanation:

A = 1R  + 2G + 3Bl

B = 2R + 3G + 4Bl

C = 3R + 4G + 1Bl

Stock  R = 14

G = 20

Bl = 14

Let say X  unit of  A  &  Y unit of B   then 14-(X + Y) units of C

14R  =  XR  + 2YR  + (14 - X - Y)3R

=> 14 = X + 2Y + 42 - 3X - 3Y

=> 2X + Y  = 28

G

20 = 2X + 3Y + 4(14 - X - Y)

=> 2X + Y  = 36

28 ≠ 36

Hence there is mistake in data

Bl

14 = 3X + 4Y + (14 - X - Y)

=> 2X + 3Y = 0

Sum of two units produced can not be Zero

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