Suppose that a new company has five employees: Zamora, Agraharam, Smith, Chou, and Macintyre. Each employee will assume one of s

Question

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Suppose that a new company has five employees: Zamora, Agraharam, Smith, Chou, and Macintyre. Each employee will assume one of s

ix responsibilities: planning, publicity, sales, marketing, development, and industry relations. Each employee is capable of doing one or more of these jobs: Zamora could do planning, sales, marketing, or industry relations; Agraharam could do planning or development; Smith could do publicity, sales, or industry relations; Chou could do planning, sales, or industry relations; and Macintyre could do planning, publicity, sales, or industry relations. Model the capabilities of these employees using a bipartite graph.

Mathematics

2 answers:

zzz [12.3K] · Answer 1 · 2026-03-09T07:48:14+03:00

Answer:

The following outlines the possible roles for each of the five employees:

Zamora: Planning, Sales, Marketing, Industry relations

Agraharam: Planning, Development

Smith: Publicity, Sales, Industry relations

Chou: Publicity, Sales, Industry relations

Macintyre: Planning, Publicity, Sales, Industry relations

The graph’s vertices represent the five employees and six responsibilities. An edge connects an employee to a responsibility that they can perform.

$T_{1}$ = {Zamora, Agraharam, Smith, Chou, Macintyre}

$T_{2}$ = {Planning, Publicity, Sales, Marketing, Development, Industry relations}

E = {(Zamora, Planning), (Zamora, Sales), (Zamora, Marketing), (Zamora, Industry relations), (Agraharam, Planning), (Agraham, Development), (Smith, Sales), (Smith, Publicity), (Smith, Industry relations), (Chou, Sales), (Chou, Publicity), (Chou, Industry relations), (Macintyre, Planning), (Macintyre, Sales), (Macintyre, Publicity), (Macintyre, Industry relations)}

Step-by-step explanation:

A bipartite graph consists of a simple graph with vertices grouped into two distinct sets $T_{1}$ and $T_{2}$ such that no edges exist among vertices within $T_{1}$ and no edges linking those in $T_{2}$ , while connections can occur between vertices from $T_{1}$ and vertices from $T_{2}$ .