Teaching DSSSB PGT Mock Test 2025 Industrial Engineering Operations Research Linear Programming

Find the dual of the following L.P.P

Maximum z = 5x1 + 2x2 + 6x3 + 4x4

Subject to: x1 + x2 + x3 + x4 ≤ 140

2x1 + 5x2 + 6x3 + x4 ≤ 200

x1 + 3x2 + x3 + 2x4 ≤ 150

All x1, x2, x3, x4 ≥ 0

1

Maximize 140 y1 + 200 y2 + 150 y3

y1 + 2y2 + y3 ≤ 5

y1 + 5y2 + 3y3 ≤ 2

y1 + 6y2 + y3 ≤ 6

y1 + y2 + 2y3 ≤ 4

All y1, y2, y3 ≥ 0

2

Minimize 140 y1 + 200 y2 + 150 y3

y1 + 2y2 + y3 ≥ 5

y1 + 5y2 + 3y3 ≥ 2

y1 + 6y2 + y3 ≥ 6

y1 + y2 + 2y3 ≥ 4

All y1, y2, y3 ≥ 0
3

Minimize 140 y1 + 200 y2 + 150 y3

y1 + 2y2 + y3 ≥ 5

y1 + 5y2 + 3y3 ≥ 2

y1 + 6y2 + y3 ≥ 6

y1 + y2 + 2y3 ≥ 4

All y1, y2, y3 ≤ 0

4

Minimize 140 y1 + 200 y2 + 150 y3

y1 + 2y2 + y3 ≤ 5

y1 + 5y2 + 3y3 ≤ 2

y1 + 6y2 + y3 ≤ 6

y1 + y2 + 2y3 ≤ 4

All y1, y2, y3 ≥ 0

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