GATE 2026 MN – Question 47
Assign four jobs J1–J4 to engineers S1–S4, one job each. Costs by row are S1:(50,50,unavailable,20); S2:(70,40,20,70); S3:(90,30,50,unavailable); S4:(70,20,60,30). Find minimum total cost as an integer.
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Correct answer: 130 to 130
Explanation
Enumerate feasible one-to-one assignments, excluding S1–J3 and S3–J4. One optimum is S1–J4 at20,S2–J3 at20,S3–J2 at30 and S4–J1 at70, totalling140; a better assignment is S1–J1 at50,S2–J3 at20,S3–J2 at30,S4–J4 at30, totalling130. Exhaustive assignment comparison confirms130 is minimal.