Consider the following LPP :
Min. Z = x1 + x2 + x3
Subject to 3x1 + 4x3 ≤ 5
5x1 + x2 + 6x3 = 7
8x1 + 9x3 ≥ 2,
x1, x2, x3 ≥ 0
The standard form of this LPP shall be :
(1) Min. Z = x1 + x2 + x3 + 0x4 + 0x5
Subject to 3x1 + 4x3 + x4 = 5;
5x1 + x2 + 6x3 = 7;
8x1 + 9x3 – x5 = 2;
x1, x2, x3, x4, x5 ≥ 0
(2) Min. Z = x1 + x2 + x3 + 0x4 + 0x5 – 1(x6) – 1(x7)
Subject to 3x1 + 4x3 + x4 = 5;
5x1 + x2 + 6x3 + x6 = 7;
8x1 + 9x3 – x5 + x7 = 2;
x1 to x7 ≥ 0
(3) Min. Z = x1 + x2 + x3 + 0x4 + 0x5 + 0x6
Subject to 3x1 + 4x3 + x4 = 5;
5x1 + x2 + 6x3 = 7;
8x1 + 9x3 – x5 + x6 = 2;
x1 to x6 ≥ 0
(4) Min. Z = x1 + x2 + x3 + 0x4 + 0x5 + 0x6 + 0x7
Subject to 3x1 + 4x3 + x4 = 5;
5x1 + x2 + 6x3 + x6 = 7;
8x1 + 9x3 – x5 + x7 = 2;
x1 to x7 ≥ 0
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