GATE 2024 AR — Planning – Question 63

Urban Land Use and Transportation · Aggregate and disaggregate transport demand models and forecasting · 2 marks · Numerical answer

An EcoCity park has inverse demand P=1500−7.5Q, where P is ticket price₹ and Q integer tickets/hour. Find maximum hourly revenue in rupees, as an integer.

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Correct answer: 75000 to 75000

Explanation

Revenue is R=PQ=1500Q−7.5Q². Its derivative is 1500−15Q, zero atQ=100. The negative second derivative confirms a maximum; 100 is also an allowed integer. Price is₹750 and revenue 750×100=₹75000/hour.

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