Minibus trips, fares and break-even on the Blantyre–Zomba route
A minibus owner operates a 14-seater minibus on the Blantyre–Zomba route. The fare is MWK 2,500 per passenger. On a particular day the minibus made 9 trips. Some trips were full, with 14 passengers, and the rest carried 9 passengers. The owner recorded 106 passengers in total. Costs for the day were: fuel at MWK 8,000 per trip, driver MWK 15,000, conductor MWK 8,000, council rank fee MWK 5,000, and maintenance estimated at MWK 6,000. The owner is considering raising the fare to MWK 3,000 but expects total passengers to fall by 15%. He wants to know how many trips were full, whether the day was profitable, and whether the fare increase is worth trying.
1. Let x be the number of full trips and y be the number of trips with 9 passengers. Form and solve simultaneous equations, then state how many of each type were made.
Read the worked answer
Let x = full trips and y = 9-passenger trips.
x + y = 9
14x + 9y = 106
Substitute y = 9 − x:
14x + 9(9 − x) = 106
14x + 81 − 9x = 106
5x = 25, so x = 5.
Then y = 9 − 5 = 4.
Check: 5 × 14 + 4 × 9 = 70 + 36 = 106. So there were 5 full trips and 4 trips with 9 passengers.
2. Calculate the daily profit at the MWK 2,500 fare.
Read the worked answer
Revenue = 106 × 2,500 = MWK 265,000.
Fuel = 9 × 8,000 = MWK 72,000.
Other costs = 15,000 + 8,000 + 5,000 + 6,000 = MWK 34,000.
Total cost = 72,000 + 34,000 = MWK 106,000.
Profit = 265,000 − 106,000 = MWK 159,000.
3. Estimate the profit if the fare rises to MWK 3,000 and passengers fall by 15%. Calculate the break-even number of passengers at each fare and advise the owner.
Read the worked answer
New passenger estimate = 106 × 0.85 = 90.1, so about 90 passengers.
Revenue = 90 × 3,000 = MWK 270,000.
Costs stay at MWK 106,000, so profit = 270,000 − 106,000 = MWK 164,000.
That is an increase of MWK 5,000, about 3.1%.
Break-even at MWK 3,000 = 106,000 ÷ 3,000 = 35.33, so 36 passengers are needed. At MWK 2,500 it is 106,000 ÷ 2,500 = 42.4, so 43 passengers are needed.
Judgement: the higher fare gives a small gain provided demand really falls by only 15%. Because 90 passengers is far above the 36-passenger break-even, the risk is limited, but the gain is small. He should trial the fare and monitor actual loads rather than assume the 15% forecast is exact.