GATE 2016 ME (ME3) – Question 65
A firm produces parts I and II using turning, milling and grinding. Required times (minutes per unit of I, II) and weekly capacity are: turning (12, 6), 6000; milling (4, 10), 4000; grinding (2, 3), 1800. Profit per unit is ₹40 for I and ₹100 for II. The maximum weekly profit is ₹______.
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Correct answer: 39000 to 41000
Explanation
Let x,y be quantities of partsI,II. Milling imposes4x+10y≤4000, so profit40x+100y=10(4x+10y)≤40000. The choice x=0,y=400 attains this bound and uses2400turning and1200grinding minutes, within capacities. Hence maximum profit is **Rs40000**; feasible points on the milling boundary can also be optimal.