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: 9

Answer

To ship $n$ units, we would need $ceiling(\frac{n}{36})$ boxes. Here, ceiling notation is more convenient than floor notation, as floor notation would require a piecewise function, with one branch for when $n$ is a multiple of $36$ and another branch for all other values of $n$.

Work Step by Step

We assume that every unit must be shipped in a box: hence, if there were even a single unit leftover, we would need to add an entire other box just to ship the one unit, even though boxes fit as many as 36 units. Contrast this with the previous problem, where there was "waste" because we could not do anything with leftover raw materials. Here, we do not wish to waste units of the product, so if the number of units is not a multiple of 36, we must use one box extra inefficiently.
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