There are four resources and four jobs to be done. Assume there must be one-to-one matching between jobs and resources. The time required for each resource to do each job is as follows: $$\begin{array} { c c c c c }
& { \text { Job (Hours) } } \
\text { Resource } & \text { A } & \text { B } & \text { C } & \text { D } \
1 & 5 & 8 & 7 & 7 \
2 & 4 & 9 & 5 & 9 \
3 & 6 & 9 & 8 & 7 \
4 & 7 & 6 & 6 & 9
\end{array}$$
After the row reduction, what is the resulting entry in the new table for assigning resource 4 to Job D?
A) 0 hours
B) 2 hours
C) 3 hours
D) 6 hours
E) 9 hours

Question

There are four resources and four jobs to be done. Assume there must be one-to-one matching between jobs and resources. The time required for each resource to do each job is as follows: $$\begin{array} { c c c c c } 
& { \text { Job (Hours) } } \
\text { Resource } & \text { A } & \text { B } & \text { C } & \text { D } \
1 & 5 & 8 & 7 & 7 \
2 & 4 & 9 & 5 & 9 \
3 & 6 & 9 & 8 & 7 \
4 & 7 & 6 & 6 & 9
\end{array}$$
After the row reduction, what is the resulting entry in the new table for assigning resource 4 to Job D?
A) 0 hours
B) 2 hours
C) 3 hours
D) 6 hours
E) 9 hours

Quizplus · Accepted Answer

Performing row reduction on the given matrix, we get the following reduced matrix.

$$\begin{array} { c c c c c } 
& { \text { Job (Hours) } } \
\text { Resource } & \text { A } & \text { B } & \text { C } & \text { D } \
1 & 0 & 2 & 1 & 4 \
2 & 0 & 4 & 0 & 4 \
3 & 1 & 4 & 2 & 2 \
4 & 0 & 0 & 0 & 4
\end{array}$$

Hence, the entry in the new table for assigning resource 4 to Job D is 4 hours. 
The best choice for assigning resource 4 to Job D is still 9 hours, as there are no other resources available that could do the job in less time.

There Are Four Resources and Four Jobs to Be Done