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Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

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BuyFindarrow_forward

Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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A set S of jobs can be ordered by writing x _ y to mean that either x = y or x must he done before y, for all x and y in S. The following is a Hasse diagram for this relation for a particular set S of jobs.

Chapter 8.5, Problem 50ES, A set S of jobs can be ordered by writing x_y to mean that either x=y or x must he done before y,
a. If one person is to perform all the jobs, one after another, find an order in which the jobs can be done.
b. Suppose enough people are available to perform any number of jobs simultaneously.
(i) If each job requires one day to perform, what is the least number of days needed to perform all ten jobs?
(ii) What is the maximum number of jobs that can be performed at the same time?

To determine

(a)

To find the order in which jobs can be done if one person performs all the jobs one after another.

Explanation

Given information:

A set S of jobs can be ordered by writing xy to mean that either x=y or x must be done before y, for all x and y in S. The following is a Hasse diagram for the relation for the particular set of jobs.

To determine

(b)

To find the least number of days needed to perform all ten jobs if each requires one day to perform and also the maximum number of jobs that can be performed at the same time.

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