Question

Part-A: Marks 141 A Textile firm is currently producing 3 different fabrics for one of its client. The client requires 5000, 5500, and 6500 meter of Cotton, Linen and Polyester, respectively. The client requires these fabrics in three different colours. The composition of the colours is represented by table 4. Blue Color Cotton Linen 50% 30% Green 30% 60% Yellow 25% 23% Table 4 The system of equation representing the aforementioned data will be: Polyester 20% 10% 52% 0.50 +0.36 +0.25Y = 5000 0.3B +0.66 + 0.23Y = 5500 0.2B +0.16 +0.52Y = 6500 Use Inverse Matrix method to determine, how many meters must be produced of each color in order to meet the client's requirement?

Answer 1

Sir, I have explained clearly,but calculation is big,If you have any doubts please let me know in comments,Thank you.

Solution- Given system of Equations: 0.5 13 + + 0.3 G + 0.25% 5000 0.313 + 0.6G + 0.23 Y 5500 02B + Oil G +0.52 Y = 6500 This can be represented in matrix form as 19 0.5 0.3 0.25 B 500 o 0.3 0.23 G ] - 5500 Oo 2 01 0.52 6 500 3X3 3x), 3X1 For the Matrix multiplication, posible; We have to write as 2: -) B 0.5 U 3 0.25 25000 G 0:3 0.6 0:23 5500 Y 3X1 0.2 0-1 0.52 6500 3x3 3X1 3x3 3x 3X1 C 3X1 First find , Inverse of matrix 0.5 0.3 0.25 0.3 OG 0.23 this matrix can be written as 0.2 0.1 0.52 ابع 3 23/100 3/10 31 15 %10 13/25

So To find inverse of this matrix, perform the following known procedure, we 다 ㅗ O 3 ôt uw ola 0 23 COO 는 13. 25 RY 2Ri ㅋ 츠 2 of gloow 10 uipo olu 23 (00 129 25 0 R2 R2 () e 10 Ri ㅕ p- 2 27 50 2 25 ( o win 13 O 5 25 R3 → R3-51 2 . 지 증 룷 한다 بیای تراری 0l 50 SO .R2 (5) R2 2. 0 5 녹 Ho s ㅋ 50 । 2} 2 기임 25 Ri Ri 3 ) R2 0 2 카 O 케능 비상 0 내리 -150250 cg

R3 Rot 3+ (4) R2 쭒 -29 १ - 10 म O - ० 2+ +O A २। 89 210 - -3 म 2 R3 → (28)83 21 70 -10 50 RI RI+म Pात 8 10 20 -१० 84 894 ११ → २) -2) २ 28१ 89 -81 89 . 1 2 glosdog 위가위 -131 ४१ (o 21 10 84 O -१० 210 Ra > R2 - 4 R3i 21 28१/११ 11489 -131/११ - 2148१ -५% 10/89 25/89 -१0/801 -131 89 5000 G । 5500 y 289 89 -110 84 -१० व 210 89 10 -40 89 210 894 6500 8 8qx5000 84 x5000-210kSSDO 289 131 X હવે .X6500 -110 q 40 ४१ X6500 89 -१० X5000+ 10x5500+210 89 x6500 89 89

to q 2224.719 = y 198000 89 345000 ។ 970000 89 38 76.405 10898.876 :. Blue colour cloth required = 2224.719 meters Green Colour Cloth required = 13876.405 meten Yellow Colour Cloth required - 1108981876 meters