1. Cost per seat analysis:
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Type P: 60200≈Rs 3.33 per seat
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Type Q: 50140=Rs 2.80 per seat
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Type R: 40125=Rs 3.125 per seat
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Type S: 3095≈Rs 3.16 per seat
Observation: Type Q is the most economical, followed by Type R.
2. Optimizing the number of buses:
Total guests to transport = 220.
We must satisfy the condition: "prefer no vacant seats". This means the total capacity of chosen buses should exactly equal 220.
Combination 1 (Using maximum Type Q):
If we use 4 buses of Type Q:
Remaining guests = 220−200=20
No bus has a capacity of exactly 20. So, this doesn't fulfill the "no vacant seats" preference perfectly.
Combination 2 (Mix of Q and R):
Let's try 2 buses of Type Q and 3 buses of Type R:
2×50+3×40=100+120=220 seats
Cost for this combination:
Combination 3 (Mix of Q and P):
Let's try 1 bus of Type P and 4 buses of Type Q:
(1×60)+(4×50)=60+200=260 (Too many seats)
(2×60)+(2×50)=120+100=220 seats
Cost:
Cost=(2×200)+(2×140)=400+280=Rs 680
Combination 4 (Best Optimization - 4 Type Q and 1 Type S?):
(4×50)+(1×30)=230 (Vacant seats)
How about 3 buses of Type Q, 1 bus of Type R, and 1 bus of Type S?
(3×50)+(1×40)+(1×30)=150+40+30=220 seats
Cost:
3. Comparison:
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Combination 2: Rs 655
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Combination 3: Rs 680
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Combination 4: Rs 640
Conclusion:
The minimum cost while maintaining zero vacant seats is Rs 640.
Correct Option: (c) Rs 640
