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:
$$\text{Customer (requirement)}\
\begin{array} { l c c c c }
&&&Customer ~3 &Customer ~4\
\text { Factory (capacity) } & \text { Custcmer } 1 ( 25 ) & \text { Customer } 2 ( 50 ) & ( 125 ) & ( 75 ) \ \text { A (100) } & \$ 15 & \$ 10 & \$ 20 & \$ 17 \ B ( 75 ) & \$ 20 & \$ 12 & \$ 19 & \$ 20 \ \text { C (100) } & \$ 22 & \$ 20 & \$ 25 & \$ 14 \end{array}$$
How many arcs will the network have?
A) 3
B) 4
C) 7
D) 12
E) 15

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:
$$\text{Customer (requirement)}\
\begin{array} { l c c c c } 
&&&Customer ~3 &Customer ~4\
\text { Factory (capacity) } & \text { Custcmer } 1 ( 25 ) & \text { Customer } 2 ( 50 ) & ( 125 ) & ( 75 ) \ \text { A (100) } & \$ 15 & \$ 10 & \$ 20 & \$ 17 \ B ( 75 ) & \$ 20 & \$ 12 & \$ 19 & \$ 20 \ \text { C (100) } & \$ 22 & \$ 20 & \$ 25 & \$ 14 \end{array}$$
How many arcs will the network have?
A) 3
B) 4
C) 7
D) 12
E) 15

Quizplus · Accepted Answer

The network will have 12 arcs, as each of the 3 factories can potentially ship to each of the 4 customers, resulting in 3 x 4 = 12 possible shipping routes or arcs.

A Manufacturing Firm Has Three Plants and Wants to Find