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Merchant ships sailing independently take 75% of the time to complete voyages compared to ships sailing in a convoy but lose 14% of their number to submarines on each voyage, whilst convoyed ships lose 5% per voyage. We start with a given fleet of merchant ships and must decide whether to use convoy for all of them or let them all sail independently. We can produce ships quickly enough to replace all those lost in convoy. Show that in the time it takes to make three convoy voyages, an independently sailing fleet will have made more voyages than a convoyed one but the position will be reversed for the time it takes to make six. What will happen over a long time?

This is what I have thought so far...If it take ships sailing independently only 75% of the time of convoys, in the time it takes the convoys to make three trips, the independently sailing ships will make 4 trips, then in the time it takes the convoys to make six trips, the independently sailing ships will make 8 trips and so on...

However a 14 % loss on 8 trips is 6.88 completed trips and a 5% loss on 6 trips is 5.7 completed trips. What am I missing?

Alex Ravsky
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mikoyan
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  • It says that they can replace all ships lost in convoy. But it says nothing about replacing independently sailing ships. I think one must make some reasonable assumption about the rate at which non-convoyed ships can be replaced. – Stephen Montgomery-Smith Dec 26 '13 at 16:33
  • I think we can assume they can also be replaced as necessary – mikoyan Dec 26 '13 at 22:44
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    But I think the point of the question is it is the attrition of non-convoyed ships that makes not using convoys the worse alternative. So I think one must assume that non-convoyed ships can only be replaced at the same rate that convoyed ships can be replaced. – Stephen Montgomery-Smith Dec 26 '13 at 22:55
  • @ Stephen Montgomery-Smith you are right 'we can produce ships quickly enough to replace all those lost in convoy' i.e. at 5 % per voyage. – mikoyan Dec 27 '13 at 12:12

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