Use this scenario for the following question(s).
With the backyard poultry craze unleashing a tidal wave of municipal code proposals, Chickenverks is poised to capitalize on the sudden demand for chicken tractors. The portable henhouses they have designed can be assembled in 10 basic steps, each with a required time and predecessor as shown in the table. There are 8 productive hours available in a day and the manufacturer wishes to produce 40 units per hour.
$$\begin{array} { | c | c | c | }
\hline \text { Task } & \text { Time } ( \mathrm { sec } ) & \text { Predecessor } \
\hline \text { A } & 25 & \cdots \
\hline \text { B } & 35 & \text { A } \
\hline \text { C } & 20 & \text { A } \
\hline \text { D } & 55 & \text { B } \
\hline \text { E } & 45 & \text { C, D } \
\hline \text { F } & 15 & \text { B } \
\hline \text { G } & 35 & \text { C } \
\hline \text { H } & 40 & \text { D, E } \
\hline \text { J } & 25 & \text { F, G } \
\hline \text { K } & 30 & \text { H, J } \
\hline
\end{array}$$
-Refer to the scenario above. What is the theoretical minimum number of stations needed?
A)3
B)4
C)5
D)6

Question

Use this scenario for the following question(s).
With the backyard poultry craze unleashing a tidal wave of municipal code proposals, Chickenverks is poised to capitalize on the sudden demand for chicken tractors. The portable henhouses they have designed can be assembled in 10 basic steps, each with a required time and predecessor as shown in the table. There are 8 productive hours available in a day and the manufacturer wishes to produce 40 units per hour.
 $$\begin{array} { | c | c | c | } 
\hline \text { Task } & \text { Time } ( \mathrm { sec } ) & \text { Predecessor } \
\hline \text { A } & 25 & \cdots \
\hline \text { B } & 35 & \text { A } \
\hline \text { C } & 20 & \text { A } \
\hline \text { D } & 55 & \text { B } \
\hline \text { E } & 45 & \text { C, D } \
\hline \text { F } & 15 & \text { B } \
\hline \text { G } & 35 & \text { C } \
\hline \text { H } & 40 & \text { D, E } \
\hline \text { J } & 25 & \text { F, G } \
\hline \text { K } & 30 & \text { H, J } \
\hline
\end{array}$$
-Refer to the scenario above. What is the theoretical minimum number of stations needed?
A)3
B)4
C)5
D)6

Quizplus · Accepted Answer

To determine the number of stations needed, we need to calculate the longest path through the graph, which represents the minimum time it will take to produce one unit. By using the critical path method, we can identify the tasks that are on the critical path, which are tasks E, H, and K. The total time for completing these tasks is 295 seconds. To produce 40 units per hour, we need to divide the available productive time (8 hours) by the time it takes to produce one unit (295 seconds), which gives us 97.6 units per day. To produce 40 units per hour, we need 40/97.6 or 0.41 stations. Since we can't have fractional stations, we round up to the nearest whole number, which gives us 1 station. So, the theoretical minimum number of stations needed is 1. However, since this is not a practical option, we can use 4 stations to produce the required number of units. This is because tasks A, B, F, and J can be grouped together and performed concurrently, as there are no dependencies between them. Similarly, tasks C, G, and D can be grouped together and performed concurrently, as there are no dependencies between them. So, we can have two stations working on these groups of tasks simultaneously, and the other two stations working on tasks E, H, and K. This would give us a production rate of 160 units per day.

Use This Scenario for the Following Question(s) -Refer to the Scenario Above