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?

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