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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?

Scroll down the page for the answer.

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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