A critical activity in a project is estimated to take $15$ days to complete at a cost of Rs. $30,000$. The activity can be expedited to complete in $12$ days by spending a total amount of Rs. $54,000$. Consider the statements $\text{P}$ and $\text{Q}$.
$\text{P}$: It is economically advisable to complete the activity early by crashing, if the indirect cost of the project is Rs. $8,500$ per day.
$\text{Q}$: It is economically advisable to complete the activity early by crashing, if the indirect cost of the project is Rs. $10,000$ per day.
Which one of the following options is CORRECT?
- Both $\mathrm{P}$ and $\mathrm{Q}$ are TRUE
- $\mathrm{P}$ is TRUE and $\mathrm{Q}$ is FALSE
- Both $\mathrm{P}$ and $\mathrm{Q}$ are FALSE
- $\mathrm{P}$ is FALSE and $\mathrm{Q}$ is TRUE