Two parallel highways connect City X to City Y, a distance of $120$ km. Highway 1 has a speed limit of $100$ km h$^{-1}$, a capacity of $8{,}000$ vehicles per day and a toll of £2 per vehicle. Highway 2 has a speed limit of $80$ km h$^{-1}$, a capacity of $12{,}000$ vehicles per day and a toll of £1 per vehicle. The total daily traffic demand between the cities is $15{,}000$ vehicles. The government values travel time at £0.10 per minute and wishes to minimise the total daily travel cost (toll plus time cost) while not exceeding the capacities. How many vehicles should be assigned to each highway each day under the optimal allocation?

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8 000 vehicles on Highway 1 and 7 000 vehicles on Highway 2

Gce Model Questions Vol1 2022 Geography Question 43

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