Question

Four jobs are on order in a factory. As on day 20 of the production calendar, the corresponding due date and work remaining to complete these jobs (in days) are given in the table below.

Job	Due date	Work remaining (in days)
M	26	5
N	24	10
O	28	10
P	31	5

Which job(s) has/have critical ratio less than unity?

• A. Job N and Job O
• B. Job M and Job N
• C. Job P
• D. Job O and Job P

Hint:

Critical ratio is \((\text{due date}-\text{today})/\text{work remaining}\); a value under 1 means the job is running behind.

Answer 1

The Correct Option is A

Step 1: Recall what critical ratio means.
The critical ratio rule scores each job as \(CR = \dfrac{\text{due date} - \text{current day}}{\text{work remaining}}\). It compares the time left before the job is due against the time actually needed to finish it. A ratio below 1 means there is less time left than the work still needs, so the job is falling behind schedule.

Step 2: Compute CR for Job M.
\(CR_M = \dfrac{26-20}{5} = \dfrac{6}{5} = 1.2\), which is above 1, so Job M still has slack.

Step 3: Compute CR for Job N.
\(CR_N = \dfrac{24-20}{10} = \dfrac{4}{10} = 0.4\), which is below 1, so Job N is behind schedule.

Step 4: Compute CR for Job O.
\(CR_O = \dfrac{28-20}{10} = \dfrac{8}{10} = 0.8\), also below 1, so Job O is behind too.

Step 5: Compute CR for Job P.
\(CR_P = \dfrac{31-20}{5} = \dfrac{11}{5} = 2.2\), well above 1, so Job P has plenty of slack.

Final Answer:
Only Job N (0.4) and Job O (0.8) come out under 1, so these are the two jobs running behind schedule. \[ \boxed{\text{Job N and Job O}} \]