Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 4 - Elementary Number Theory and Methods of Proof - Exercise Set 4.5 - Page 197: 8

Answer

With $n$ pounds of raw material, $floor(\frac{n}{7})$ units can be produced. Floor notation is more convenient than ceiling notation, as ceiling notation would lead to a piecewise function, with one branch for when $n$ is a multiple of seven and another branch for all other values of $n$.

Work Step by Step

The motivation behind this answer is that one cannot manufacture an entire unit with less than seven pounds of material, nor can one manufacture "partial units." Hence, we divide the number of pounds of raw material by seven and then round down (using the floor function) to get the correct number of units. Note that, in general, $floor(\frac{n}{7})\ne \frac{floor(n)}{7}$: the latter will typically lead to a fractional result, which is not what we want.
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