Weekly puzzle 13
Desert Survival
An explorer named Marco wants to cross an Australian desert on foot. The track will begin in the outback at the aboriginal village of Kwazi and takes six days. However, one man can only take enough food to last him four days.
Fortunately, Marco can hire porters from Kwazi to assist him. Each porter cost $100 per day that he is away from the village. What is the least possible cost to Marco of hiring enough porters so that he can cross the desert and the porters can return home safely?
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C’mom Andrew, I invest a lot of work trying to obfuscate my answers… You can say I work a lot to provide no work, you know!? :-)
In my defense, let me say this: if Marco is allowed to pay by the hour of transport, each day they walk 12 hours (meaning the porter will won $100/12 by the hour and after walking 12h, they earn the $100 even if they returned to the village after only half a day), and their food consume is proportional to the walking hours (they don’t need to consume for the hours of rest), then it is possible for Marcus to pay to the Porters LESS THAN $600! I’ll write here the value if you already know this, otherwise, I’ll leave this as problem to you to solve if you are interested.
Other ways of presenting the problem in a form that allows my new value is to consider hours instead of days (payed $100 by hour, each traveler are able to transport 4 hours of food… lame, I know), or to scale the problem (multiplying the days of travel and the food each one can carry by a constant, and divide the pay per day by the same value). My motivation was a point of contention with my friend were I stressed to him that to leave the food at places or to transport it always, HAS implications… but actually, the way how the problem is formulated negates that difference. I now believe $600 is really the best solution because my solution is now optimal… and in the conditions of the problem, that’s the value to which it leads me.
Ok. ignore the last question. Got it.
Do the porters have to return home? Or can they cross the desert with him?
Even if $600 were correct you would get 1/10 in a maths exam for providing no working!
Hmmm… let me see… the full travel lasts 6 days and the cost of each porter per day is $100, so doing the math, the least possible cost is… 6x$100=$600
:-D
Well, is is well know that I never have it right first time, so maybe there is a strategy to get a better result (also, I got it when I was doing the… well, what we do everyday in specific times to became lighter, beside to breath). However I have a friend which got the same value while using a different strategy than mine (I think his is more elegant actually), so maybe that’s the best value. I would hate the idea of trying to find a new “pun” to justify a different value other than $600.
PS.: Forgive me the spoiling which reveals more of my solution than I would have liked…
Yes, both are acceptable.
Can the porters leave behind (or forward) food or must they keep transport it always?