A high definition television manufacturer in Asia wants to develop a new smart television as fast as possible using Program Evaluation and Review Technique (PERT) and must complete the design and testing work first. The objective is to be the first to market the most innovative smart television on the planet and capture the first adopter market share. The manufacturer has determined the following activities, precedence relationships, and time estimates in days for the project:
$\begin{array}{rcccr}& \text { Immediate } & \text { Optimistic } & \text { Most Likely } & \text { Pessimistic } \
\text { Activity } & \text { Predecessors } & t_{o} & t_{m} & t_{p}\\hline
a & \text { none } & 4 & 6 & 7 \
\mathrm{~b} & \mathrm{a} & 1 & 2 & 3 \
\mathrm{c} & \mathrm{a} & 5 & 5 & 5 \
\mathrm{~d} & \mathrm{~b} & 7 & 9 & 12 \
\mathrm{e} & \mathrm{b} & 2 & 4 & 8 \
\mathrm{f} & \mathrm{c} d & 6 & 9 & 10
\end{array}$ Solutions are at the end of questions
-The expected duration of the critical path in days is _____.
A) less than or equal to 20 days
B) greater than 20 but less than or equal to 25 days
C) greater than 25 but less than or equal to 30 days
D) greater than 30 days

Question

A high definition television manufacturer in Asia wants to develop a new smart television as fast as possible using Program Evaluation and Review Technique (PERT) and must complete the design and testing work first. The objective is to be the first to market the most innovative smart television on the planet and capture the first adopter market share. The manufacturer has determined the following activities, precedence relationships, and time estimates in days for the project:
 $\begin{array}{rcccr}& \text { Immediate } & \text { Optimistic } & \text { Most Likely } & \text { Pessimistic } \
\text { Activity } & \text { Predecessors } & t_{o} & t_{m} & t_{p}\\hline
a & \text { none } & 4 & 6 & 7 \
\mathrm{~b} & \mathrm{a} & 1 & 2 & 3 \
\mathrm{c} & \mathrm{a} & 5 & 5 & 5 \
\mathrm{~d} & \mathrm{~b} & 7 & 9 & 12 \
\mathrm{e} & \mathrm{b} & 2 & 4 & 8 \
\mathrm{f} & \mathrm{c} d & 6 & 9 & 10
\end{array}$ Solutions are at the end of questions 
-The expected duration of the critical path in days is _____.
A) less than or equal to 20 days
B) greater than 20 but less than or equal to 25 days
C) greater than 25 but less than or equal to 30 days
D) greater than 30 days

Quizplus · Accepted Answer

To find the expected duration of the critical path, we first calculate the expected time ($t_e$) for each activity using the formula $t_e = (t_o + 4t_m + t_p) / 6$. Then, we identify the critical path by adding the expected times of the longest path(s) through the network.- For activity a: $t_e = (4 + 4*6 + 7) / 6 = 6.5$ days- For activity b: $t_e = (1 + 4*2 + 3) / 6 = 2$ days- For activity c: $t_e = (5 + 4*5 + 5) / 6 = 5$ days (since $t_o = t_m = t_p$, $t_e = t_m$)- For activity d: $t_e = (7 + 4*9 + 12) / 6 = 9$ days- For activity e: $t_e = (2 + 4*4 + 8) / 6 = 4$ days- For activity f: $t_e = (6 + 4*9 + 10) / 6 = 9$ daysThe paths through the network are:- a-b-d-f with a total expected time of $6.5 + 2 + 9 + 9 = 26.5$ days- a-b-e with a total expected time of $6.5 + 2 + 4 = 12.5$ days- a-c-f with a total expected time of $6.5 + 5 + 9 = 20.5$ daysThe longest path is a-b-d-f, with an expected duration of 26.5 days, which falls into the range of "greater than 25 but less than or equal to 30 days".

A High Definition Television Manufacturer in Asia Wants to Develop