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.
Answers
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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