Answer:
a. $1.03
b. $0.93
c. 0.98
d. 2 workers
Step-by-step explanation:
a. Given that:
- 1 computer : 1 worker : inventory 150 items per hour
- 1 computer : 2 workers : inventory 200 items per hour
- 1 computer : 3 workers : inventory 220 items per hour
- 1 computer : 4+ workers : fewer than 235 items per hour
- Cost: $100 per computer ; $25 per worker
The fixed production factor in the warehouse is the computer used:
-One computer used, but the number of users is varied to inventory a specified number of items.
-The variable production factor is the number of workers assigned per one computer.
#The cost of inventorying a single item by one worker is:
![Cost=\frac{C_{pc}+Wage}{Items} \ , C_{pc}=\$125\\\\Cost_1=\frac{125+30}{150}\\\\\\=1.03](https://tex.z-dn.net/?f=Cost%3D%5Cfrac%7BC_%7Bpc%7D%2BWage%7D%7BItems%7D%20%5C%20%2C%20C_%7Bpc%7D%3D%5C%24125%5C%5C%5C%5CCost_1%3D%5Cfrac%7B125%2B30%7D%7B150%7D%5C%5C%5C%5C%5C%5C%3D1.03)
Hence, the cost of inventorying a single item is $1.03
b. Using the information provided above, the cost of inventorying a single item when two workers are assigned is :
![Cost=\frac{C_{pc}+Wage}{Items} \ , C_{pc}=\$125\\\\Cost_2=\frac{125+2\times30}{200}\\\\\\=0.925](https://tex.z-dn.net/?f=Cost%3D%5Cfrac%7BC_%7Bpc%7D%2BWage%7D%7BItems%7D%20%5C%20%2C%20C_%7Bpc%7D%3D%5C%24125%5C%5C%5C%5CCost_2%3D%5Cfrac%7B125%2B2%5Ctimes30%7D%7B200%7D%5C%5C%5C%5C%5C%5C%3D0.925)
Hence, the cost of inventorying a single item is $0.93
c.Using the information provided above, the cost of inventorying a single item when three workers are assigned is :
![Cost=\frac{C_{pc}+Wage}{Items} \ , C_{pc}=\$125\\\\Cost_3=\frac{125+3\times30}{220}\\\\\\=0.98](https://tex.z-dn.net/?f=Cost%3D%5Cfrac%7BC_%7Bpc%7D%2BWage%7D%7BItems%7D%20%5C%20%2C%20C_%7Bpc%7D%3D%5C%24125%5C%5C%5C%5CCost_3%3D%5Cfrac%7B125%2B3%5Ctimes30%7D%7B220%7D%5C%5C%5C%5C%5C%5C%3D0.98)
Hence, the cost of inventorying a single item is $0.98
d. To determine the most cost-effective job assignment, we calculate the cost of 4+ workers.
Take any number less than 235(say 234) as the inventory units:
![Cost=\frac{C_{pc}+Wage}{Items} \ , C_{pc}=\$125\\\\Cost_4=\frac{125+4\times30}{234}\\\\\\=1.05](https://tex.z-dn.net/?f=Cost%3D%5Cfrac%7BC_%7Bpc%7D%2BWage%7D%7BItems%7D%20%5C%20%2C%20C_%7Bpc%7D%3D%5C%24125%5C%5C%5C%5CCost_4%3D%5Cfrac%7B125%2B4%5Ctimes30%7D%7B234%7D%5C%5C%5C%5C%5C%5C%3D1.05)
From our calculations, it's clear that two workers per computer costs the least amount($0.93) per unit item. Hence, it is best to assign two workers per computer.