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# Another spin on a classic: Transporting Apples

Best Answer plasmid, 23 June 2013 - 04:10 PM

Spoiler for Let's work backwards
Go to the full post

20 replies to this topic

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Posted 21 June 2013 - 11:39 PM

A truck driver needs to transport 3000 apples to a local business.  His truck can only hold 1000 apples.  However, complicating the apple delivery is the drivers habit of eating his delivery apples while driving.  If there are any apples in the truck, the driver will manage to eat 1 apple per mile.

What is the best means for the driver getting the apples to the market (eating the fewest apples while making the delivery)?

Assume that there is a safe fruit storage points along the way and that time or gas is of no issue.

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### #2 bonanova

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Posted 22 June 2013 - 08:54 PM

Assume the business is 3000 miles away. The driver will consume all the apples.
Assume the business is one inch away. Almost any scheme delivers all the apples.

So, don't we need to know how far away the business is?
Or should we take the distance to be x<3000 and optimize for each x?
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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Posted 22 June 2013 - 11:06 PM

Assume the business is 3000 miles away. The driver will consume all the apples.
Assume the business is one inch away. Almost any scheme delivers all the apples.

So, don't we need to know how far away the business is?
Or should we take the distance to be x<3000 and optimize for each x?

oops.  I meant to also state that the business is 1000 miles away.

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### #4 plasmid

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Posted 23 June 2013 - 07:09 AM

Does the driver start off with 3000 apples and need to deliver as many of them as possible to his destination, or does he need to end up with 3000 apples at his destination while starting the delivery with as few apples as possible?
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Posted 23 June 2013 - 03:10 PM

Does the driver start off with 3000 apples and need to deliver as many of them as possible to his destination, or does he need to end up with 3000 apples at his destination while starting the delivery with as few apples as possible?

He needs to deliver 3000 apples from some unlimited supply of apples eating as few of them along the way as possible.

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### #6 plasmid

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Posted 23 June 2013 - 04:10 PM   Best Answer

Spoiler for Let's work backwards

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### #7 vinay.singh84

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Posted 23 June 2013 - 08:41 PM

Assume the business is 3000 miles away. The driver will consume all the apples.
Assume the business is one inch away. Almost any scheme delivers all the apples.

So, don't we need to know how far away the business is?
Or should we take the distance to be x<3000 and optimize for each x?

oops.  I meant to also state that the business is 1000 miles away.

How does that qualify as local?

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Posted 23 June 2013 - 10:50 PM

Assume the business is 3000 miles away. The driver will consume all the apples.
Assume the business is one inch away. Almost any scheme delivers all the apples.

So, don't we need to know how far away the business is?
Or should we take the distance to be x<3000 and optimize for each x?

oops.  I meant to also state that the business is 1000 miles away.

How does that qualify as local?

it is all a matter of scale, semantics, and poor translations.

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### #9 bonanova

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Posted 24 June 2013 - 05:56 AM

Assume the business is 3000 miles away. The driver will consume all the apples.
Assume the business is one inch away. Almost any scheme delivers all the apples.
So, don't we need to know how far away the business is?
Or should we take the distance to be x<3000 and optimize for each x?

oops.  I meant to also state that the business is 1000 miles away.
How does that qualify as local?

The OP might mean the store sells only to nearby customers.
As opposed to a national chain or a wholesale distributor.

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

### #10 dgreening

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Posted 24 June 2013 - 04:13 PM

The problem statement says

• "His truck can only hold 1000 apples."

​the update says that the store is 1000 miles away

If the driver starts with a full load [1000 apples] and drives 1000 miles, he will have 0 apples left upon arrival.

Thus, unless he can ferry apples to some point(s) in between and then move these forward, there is no way to every deliver even 1 apple.

If we assume that there is a point halfway [500 miles] then he could do the following:

• leave the warehouse with 1000 apples
• drive 500 miles [now has 500 apples]
• leave the apples at the halfway point [now has 500 apples]
• drive back to the ware house
• leave the warehouse with 1000 apples
• drive 500 miles [now has 500 apples]
• Picks up 500 the apples at the halfway point [now has 1000 apples in the truck and 0 apples at the halfway point]]
• Drives the remaining 500 miles to the store and delivers 500 apples

Thus for 2 trips[500 and 1000 miles one way (3000 miles total round trip)] 500 apples can be delivered

to deliver 3000 apples would require:

• an interim storage area at 500 miles
• 6 "short" round trips between the warehouse and the interim storage area [1000 miles R/T each]
• 6 "long" round trips from the warehouse [stopping at the interim storage area to reload] to the store [2000 miles R/T each]

Notes:

• you can break this up many ways
• it is not clear what the optimal interim storage area distance [from the ware house] is [and if more than 1 helps]

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