GATE 2021 PI – Question 42
Products P,Q earn unit profits 4,5. Per-unit resource uses (P,Q) and availability are manpower (1,1):10; R1 (1,2):18; R2 (2,1):18. Find maximum profit.
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Correct answer: (B) 48
Explanation
Maximize $4P+5Q$ with P+Q ≤ 10, P+2Q ≤ 18, 2P+Q ≤ 18, P,Q ≥ 0. Feasible corner profits: (0,0)→0, (9,0)→36, (8,2)→42, (2,8)→48, (0,9)→45. The two raw-material boundaries intersect at (6,6), infeasible for manpower. Maximum is **48, B**, at (2,8).