24. Mungo Park
The bold explorer Mungo Park has a six day journey across country. One person can only carry enough food for four days so Mungo knows that he will need some help. Local porters can be hired for $100 a day. How can Mungo arrange it for least cost so that he can make the journey and the porters can get back home?
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He hires two porters, A and B. They all stock up with food so at the start of day 1 the supplies look like this:
M(4) + A(4) + B(4)
at the end of day 2 they have
M(3) + A(3) + B(3)
B gives 1 day's supply to M and 1 day's supply to A so at the start of day 2 the situation is
M(4) + A(4) + B(1)
B goes home (he will have been away for 2 days, costing $200) and Mungo and A press on. At the end of day 2 we have
M(3) + A(3)
A gives one day's supply to M and at the start of day 3 the situation is
M(4) + A(2)
So A has enough food to get home ( he will have been away for four days, costing $400) and Mungo has enough to complete the journey. The cost, then, is $600.
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