First of all, please don't think bad of this question. And i'm really sorry for this stupid question.
We know $\dfrac 0 0$ is not a number, undefined, undetermined, meaningless or whatever. I just want to know, if i multiply this expression by $0$, could it gives me the answer $0$?
I mean :
$$\frac{0}{0}\times 0=0$$ by inverse multiplication
The reason i'm asking this question, because i found this problem when i was calculating project time, project cost on project planning involving the PERT/CPM.
Just to the point, i will take one activity that makes me confused.
given :
- Normal Time $=1$
- Normal Cost $=5$
- Crash Time $=1$
- Crash Cost $=5$
- Time Reduction $0$
The formula of Slope is $$\Delta C=\frac{\text{Crash Cost $-$ Normal Cost}}{\text{Normal Time $-$ Crash Time}}$$
Hence, we obtain
$$\frac{5-5}{1-1}=\frac 0 0$$
My goal is calculating The Optimal Cost, i can't show all the result, because there are too many numbers and tables. (Sorry)
But, with CPM (Critical Path Method using Network Graph), i found the optimal cost for that activity must be five, and this referring to my $\Delta C$. And i'm sure it must be five because I'm very careful when calculating it.
Then, when i use the fact of the optimal cost formula that is:
Optimal Cost $=$ Normal Cost $+$ (slope ($\Delta C$) $\times$ Time Reduction)
We have :
Optimal Cost $=5+\dfrac{0}{0}\times 0$
Since with CPM my activity is five, the term $\dfrac{0}{0}\times 0$ must be $0$
It's weird, does $0$ has multiplication inverse?
It looks like againts the rule. Please give me the reason about, how does this is make sense?
Thanks in advance