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# The dual linear program of maximize -9x1-5x29x3-4x4 subject to 3x1-5x2

INSTRUCTIONS TO CANDIDATES

QUESTION 1

The dual linear program of

maximize -9x1-5x29x3-4x4

subject to 3x1-5x2

+ 2x4 = 4

= 3

5x1 + x27x3 + 4x4

-6x15x29x3 - 4X4 S-1

-9x18x23x3 -3X4 S-5

X2 X4 20

is

minimize

4X1+ 3X2 X3 -5x4

subject to 3y+ 5y2-6у3-9Y4

✓ -9

-5y1 + Y2-5y3-8Y4

✓ -5

-7y2 +9y3 - 3Y4

v-9

2y1+ 4у2-4у3 - 3Y4

v-4

QUESTION 2 For the linear program maximize - -4x2 X3 + 4x4 subject to 2x12x2 - 8X3 +7x4 ≤-2 -2x2+7x3-3X4 S-7 3x1+5x24x3 - 7x4 ≤ 3 X1 +5x3 + 5x4 ≤ 16 X1, X2, X3, X4 20 and feasible solution x = (0, 4, 1, 2), which of the following statements is correct? There does not exist any dual solution satisfying the complementary slackness conditions with x. There exist infinitely many dual solutions satisfying the complementary slackness conditions with x'. There exists a unique dual solution y satisfying the complementary slackness conditions with x, and y is feasible for the dual linear program. There exists a unique dual solution y satisfying the complementary slackness conditions with x, but y is not feasible for the dual linear program.

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