GATE 2024 MA – Question 58

Linear Programming · Duality · 2 marks · Numerical answer

Maximize 10x+6y−8z with 5x−2y+6z≤20, 10x+4y−6z≤30, x,y,z≥0. Find maximum to two decimals.

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Correct answer: 56.66 to 56.68

Explanation

Multiply the first bound by 1/3 and the second by 5/3. Their sum bounds (55/3)x+6y−8z≤170/3. Since x≥0, the objective is at most 170/3. Feasible (x,y,z)=(0,25,35/3) attains it with both constraints tight. Maximum **56.67**.

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