A manufacturing firm has three plants and wants to find the most efficient means of meeting the requirements of its four customers. The relevant information for the plants and customers, along with shipping costs in dollars per unit, are shown in the table below:
$$\text{Customer (requirement)}\
\begin{array} { l c c c c }
&&&Customer ~3 &Customer ~4\
\text { Factory (capacity) } & \text { Custcmer } 1 ( 25 ) & \text { Customer } 2 ( 50 ) & ( 125 ) & ( 75 ) \ \text { A (100) } & \$ 15 & \$ 10 & \$ 20 & \$ 17 \ B ( 75 ) & \$ 20 & \$ 12 & \$ 19 & \$ 20 \ \text { C (100) } & \$ 22 & \$ 20 & \$ 25 & \$ 14 \end{array}$$
Which type of network optimization problem is used to solve this problem?
A) Maximum-Cost Flow problem
B) Minimum-Cost Flow problem
C) Maximum Flow Problem
D) Minimum Flow Problem
E) Shortest Path Problem

Question

A manufacturing firm has three plants and wants to find the most efficient means of meeting the requirements of its four customers. The relevant information for the plants and customers, along with shipping costs in dollars per unit, are shown in the table below:
$$\text{Customer (requirement)}\
\begin{array} { l c c c c } 
&&&Customer ~3 &Customer ~4\
\text { Factory (capacity) } & \text { Custcmer } 1 ( 25 ) & \text { Customer } 2 ( 50 ) & ( 125 ) & ( 75 ) \ \text { A (100) } & \$ 15 & \$ 10 & \$ 20 & \$ 17 \ B ( 75 ) & \$ 20 & \$ 12 & \$ 19 & \$ 20 \ \text { C (100) } & \$ 22 & \$ 20 & \$ 25 & \$ 14 \end{array}$$
Which type of network optimization problem is used to solve this problem?
A) Maximum-Cost Flow problem
B) Minimum-Cost Flow problem
C) Maximum Flow Problem
D) Minimum Flow Problem
E) Shortest Path Problem

Quizplus · Accepted Answer

This is a Minimum-Cost Flow problem because the goal is to find the most efficient (least cost) way to distribute goods from multiple sources (plants) to multiple destinations (customers) while considering the capacities of the sources and the requirements of the destinations.

A Manufacturing Firm Has Three Plants and Wants to Find