Question

Activity $P$ is followed by activity $Q$ which in turn is followed by activity $R$. The direct cost of these activities in relation to the choice of feasible durations table is given below:

	Activity P	Activity Q	Activity R
Duration in days	7	6	5	8	7	6	9	8	7
Direct cost Rs 1000	12	14	15	20	23	27	40	42	45

For all the three activities taken together the minimum possible direct cost for a total duration of $21$ days will be:

• A. $81,000$
• B. $79,000$
• C. $77,000$
• D. $78,000$

Answer 1

The correct option is C $77,000$

Initially
$\begin{array}{c}P\to 7\text{days}\\ Q\to 8\text{days}\\ R\to 9\text{days}\end{array}\}24\text{days}$

Cost slope for activity P & R are 2000 and for Q is 3000
$P$ & $R=\frac{(14-12)}{7-6}1000$ & $\frac{42-40}{9-8}\times 1000=2000$
$Q=\frac{(23-20)1000}{8-7}=3000$
Crash P & R by $1$ day now project duration is $22$ days now P has least cost slope $\frac{(15-14)}{6-5}1000=1000$
For 21 days $15,000+20,000+42,000=77,000$