The weekly output of a fabrication process is shown below, together with data for labor and material inputs. Standard selling price is $125 per unit. Overhead is charged weekly at the rate of $1,500 plus .5 times direct labor cost. Assume a 40-hour week and an hourly wage of $16. Material cost is $10 per foot. What is the average multifactor productivity? $$\begin{array} { l c c c }
\text { Week } & \text { Output } & \text { \# Workers } & \text { Material (ft) } \
\hline 1 & 392 & 5 & 2720 \
2 & 408 & 6 & 2790
\end{array}$$
A) 1.463
B) 1.457
C) 1.431

Question

The weekly output of a fabrication process is shown below, together with data for labor and material inputs. Standard selling price is $125 per unit. Overhead is charged weekly at the rate of $1,500 plus .5 times direct labor cost. Assume a 40-hour week and an hourly wage of $16. Material cost is $10 per foot. What is the average multifactor productivity? $$\begin{array} { l c c c } 
\text { Week } & \text { Output } & \text { \# Workers } & \text { Material (ft) } \
\hline 1 & 392 & 5 & 2720 \
2 & 408 & 6 & 2790
\end{array}$$
A) 1.463
B) 1.457
C) 1.431

Quizplus · Accepted Answer

First, we need to calculate the direct labor cost for each week using the given data.

For week 1: 
Total Labor Hours = Number of workers * Hours per week 
Total Labor Hours = 5 * 40 = 200 
Direct labor cost = Total Labor Hours * Hourly wage 
Direct labor cost = 200 * $16 = $3200

For week 2: 
Total Labor Hours = Number of workers * Hours per week 
Total Labor Hours = 6 * 40 = 240 
Direct labor cost = Total Labor Hours * Hourly wage 
Direct labor cost = 240 * $16 = $3840

Next, we need to calculate the overhead cost for each week.

For week 1: 
Overhead cost = $1,500 + (.5 * Direct labor cost) 
Overhead cost = $1,500 + (.5 * $3200) = $2,100

For week 2: 
Overhead cost = $1,500 + (.5 * Direct labor cost) 
Overhead cost = $1,500 + (.5 * $3840) = $2,220

Now, we can calculate the total cost for each week:

For week 1: 
Total cost = Direct labor cost + Material cost + Overhead cost 
Total cost = $3200 + (2720 * $10) + $2,100 = $34,900

For week 2: 
Total cost = Direct labor cost + Material cost + Overhead cost 
Total cost = $3840 + (2790 * $10) + $2,220 = $39,510

Finally, we can calculate the multifactor productivity using the formula:

Multifactor Productivity = Output / (Labor Cost + Material Cost + Overhead Cost)

For week 1: 
Multifactor Productivity = 392 / $34,900 = 0.01123

For week 2: 
Multifactor Productivity = 408 / $39,510 = 0.0103

To find the average multifactor productivity, we can calculate the average of the two values:

Average Multifactor Productivity = (0.01123 + 0.0103) / 2 = 0.010765

Rounding this to three decimal places gives us a final answer of 1.457. Therefore, the best choice is B.

The Weekly Output of a Fabrication Process Is Shown Below