Page 65 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes Step 4: First iteration of Simplex Method.
BV CB XB Y1 Y2 Y3 S1 S2 S3 S4 S5 S6 S7 Min. Ratio
S1 0 36 0.10 0.12 0.15 1 0 0 0 0 0 0 36/0.15 = 240
S2 0 30 0.06 0.05 0.09 0 1 0 0 0 0 0 30/0.09 = 33.3
S3 0 37 0.18 1 0.07 0 0 1 0 0 0 0 37/0.08 = 529
S4 0 38 0.13 0.10 0.08 0 0 0 1 0 0 0 38/0.08 = 475
S5 0 200 1 0 0 0 0 0 0 1 0 0 200/0 = –
S6 0 100 0 1 0 0 0 0 0 0 1 0 100/0 = –
S7 0 180 0 0 1 0 0 0 0 0 0 1 180/1 =
180(KR)?
Zj 0 0 0
Cj 10 12 15
Zj – –10 –12 –15
Cj
( KC)
Therefore, Z = C X
B B
= (0 × 36) + (0 × 30) + (0 × 37) + (0 × 38) + (0 × 200) + (0 × 100) + (0 × 180)
= 0 + 0 + 0 + 0 + 0 + 0 + 0
= 0
Step 5: Second iteration of Simplex Method.

BV CB XB Y1 Y2 Y3 S1 S2 S3 S4 S5 S6 S7 Min.
Ratio
S1 0 36 – 0.10– 0.12–0 0.15–0 – – – – – – – 9/0.12 =
180(0.15) 0(0.15) (0.15) = (0.15) = 75
= 9 = 0.10 0.12 0
S2 0 30 – 0.06–0 0.05–0 0.09 – 1 – – – – – – – 13.80/0.05
180(0.09) (0.09) = (0.09) = (0.09) = = 276
= 13.8 0.06 0.05 0
S3 0 37 – 180 0.18–0 1–0(0.07) 0.07–1 – – – – – – – 24.4/1 =
(0.07)= (0.07) = 1 (0.07) = 24.4(KR)?
24.4 = 0.18 0
S4 0 38 – 180 0.13–0 0.10 – 0 0.08 – 1 – – – – – – – 23.6/0.10
(0.08) = (0.08) (0.08) (0.08) = = 236
23.6 = 0.13 = 0.10 0
S5 0 200–180 0.10 (0) 0 – 0 = 0 0 – – – – – – – (0) = 200
= 1
S6 0 100–180 0 – 0 = 0 1 – 0 0 – – – – – – – 100/1=
(0) = 100 (0)= 1 100
Y3 15 180/1 = 0 0 1/1 = 1 – – – – – – –
180
Zj 0 0 15
Cj 10 12 15
Zj – Cj –10 –12 0
( KC)
Therefore, Z = C X
B B
= (0 × 9) + (0 × 3.8) + (0 × 24.4) + (0 × 23.6) + (0 × 200) + (0 × 100) + (15 × 180)
= 2700

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