GATE 2022 MA – Question 57

Linear Programming · Transportation and Assignment · 2 marks · Numerical answer

Three companies C₁,C₂,C₃ bid for three jobs J₁,J₂,J₃, each company taking one job. Cost rows are C₁:(10,12,8),C₂:(9,15,10),C₃:(15,10,9). Find the minimum assignment cost.

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Correct answer: 27 to 27

Explanation

Enumerate job permutations (123),(132),(213),(231),(312),(321) for the companies. Their totals are 34,30,30,37,27,38. The minimum assigns C₁→J₃,C₂→J₁,C₃→J₂, costing 8+9+10=**27**.

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