GATE 2020 ME (ME1) – Question 57
Shveta and Ashok independently produce A and B in two states, selling at ₹2000/kg and ₹3000/kg respectively. Each maximizes daily revenue by linear programming. Daily A production must be at least B production, and B is limited to 10 kg/day. State regulations restrict Shveta’s A production to less than 20 kg/day and Ashok’s to less than 15 kg/day. Demand is high and everything produced is sold. Find the absolute difference in optimal daily revenue (thousand rupees), to two decimals.
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Correct answer: 9.9 to 10.1
Explanation
All coefficients are positive, so choose B=10 and each business’s maximum allowed A. Shveta obtains 2000(20)+3000(10)=70000; Ashok obtains 2000(15)+3000(10)=60000. Their difference is 10000 rupees=**10.00 thousand rupees**. Both optima satisfy A≥B. The source says “less than” the A limits. With strict inequalities a maximum is not attained; the displayed result is the limiting revenue difference, or the usual LP interpretation with inclusive capacity bounds.