220 guests are to be transported from A to B. Any number of buses of
the following passenger carrying capacities are available.
Type P: 60, Type Q : 50, Type R : 40, Type S : 30
The cost per trip for a bus of each of these types is given as follows:
Type P: Rs 200, Type Q: Rs 140, Type Rt Rs :125, Type S: Rs 95
No buses can be overloaded and, prefer no vacant seats in each trips
What is the minimum possible cost for the trip?
🎥 Video solution / Text Solution of this question is given below:
We want exactly 220 seats with minimum cost.
Cost per seat:
P: 200/60 = 3.33
Q: 140/50 = 2.80
R: 125/40 = 3.12
S: 95/30 = 3.16
→ Cheapest is Type Q, then Type R.
Try to maximize Q + R combination to make exactly 220.
Check combinations:
• 4Q + 1R = 4×50 + 40 = 240 (too high)
• 3Q + 2R = 150 + 80 = 230 (too high)
• 3Q + 1R = 150 + 40 = 190 → remaining 30 → 1S
Total = 3Q + 1R + 1S = 150 + 40 + 30 = 220 ✔
Cost = 3×140 + 125 + 95
= 420 + 125 + 95
= Rs 640