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Consider the following design problem concerning implementation of virtual- circut service. If virtual circuits are used internal to the subnet, each data packet must have a 3-byte header and each router must tie up 8 bytes of storage for circuit identification. If datagrams are used internally, 15 byte headers are needed but no router table space is required. Transmission capability costs 1 cent per $10^6$ bytes, per hop. Very fast router memory can be  purchased for 1 cent per byte and is depreciated over two years, assuming a 40 hour business week. The statistically average runs for 1000 sec. in which time 200 packets are transmitted. The mean packet requires four hops. Which implementation is cheaper and why?

mean packet requires 4 hops means 3 router in between the source and destination.

header size =3 bytes for each packet so overhead for 200 packets=200*3=600 bytes

routers have 8 bytes for circuit identification means total=8*3=24 bytes

let the data size=D,so packet size=(D+3) bytes

transmission cost =1 cent per 10^6 bytes per hop=>transmission cost for 1 Byte,per hop=10^-6 cent

transmission cost for 1 packet=(D+3)*number of hops*transmission cost of 1 hop

=>(D+3)*4*10^-6 cents

so total costs=200*(D+3)*4*10^-6 cents=>8*(D+3)*10^-4 cents

in the second case header size is 15 bytes for each packet so total header overhead=200*15=3000 bytes

no router table space is required means space=0 byte

cost for 1 packet=(D+15)*4*10^-6 cents

=>for 200 packets=>200*(D+15)*4*10^-6 cents=8*(D+15)*10^-4 cents

so from above discussion we can say first one implementation is cheaper
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I have a minor doubt. I think it should be 5 routers for 4 hops. Please correct me if I am wrong.
actually nothing is said about source and destination and packet goes through 4 hops means source put the packet onto the link and it goes through 3 routers and finally to the destination so total 4 hops it has gone through. If there is  condition that in between source and destination it goes through 4 hops then we can say there will be 5 routers