### 23.2.04

## The miller and the donkey

**A miller intends to carry 100 bags of wheat, contends each one 100 kg, from his house up to a mill that is distant 100 km from there. For such uses a donkey that he knows not to support a load more than 100 kg. However the problem is that the donkey when loaded it needs to ingest 1 kg of wheat for each km that it covers.**

The question is: Which is the biggest amount of wheat that the miller will make to arrive to the mill?

Note 1: The bags have null weight.

Note 2: The donkey without load does not consume wheat none "The question is: Which is the biggest amount of wheat that the miller will make to arrive to the mill?

Note 1: The bags have null weight.

Note 2: The donkey without load does not consume wheat none "

(Courtesy of Engº X of the Department of Physics of the Coimbra Univ., Portugal)

**Theoretic solution**

In theory the biggest quantity of wheat is = 3 647,428 kg

This result was reached by a Pascal programme, but I wanted an equation as solution.

I have obtained the equation

**Y = Yo / e**that gives the result approximative of 3 678,794 kg. This result exceeds in 0,86 % the theoric limit. I wanted a more exact equation. Will be this possible?

Reply to:

*manuelcruzsousa@sapo.pt*

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