Question

Imagine you have some workers and some handheld computers that you can use to take inventory at a warehouse. There are diminishing returns to taking inventory. If one worker uses one computer, he can inventory 150 items per hour. Two workers sharing a computer can together inventory 200 items per hour. Three workers sharing a computer can together inventory 220 items per hour. And four or more workers sharing a computer can together inventory fewer than 235 items per hour. Computers cost $125 each and you must pay each worker $30 per hour.

a. If you assign one worker per computer, what is the cost of inventorying a single item?

b. What if you assign two workers per computer? What is the cost of inventorying a single item?

c. What if you assign three workers per computer?

d. How many workers per computer should you assign if you wish to minimize the cost of inventorying a single item?

Answer 1

a. $1.03

b. $0.93

c. 0.98

d. 2 workers

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=(C_(pc)+Wage)/(Items) \ , C_(pc)=\$125\\\\Cost_1=(125+30)/(150)\\\\\\=1.03`

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=(C_(pc)+Wage)/(Items) \ , C_(pc)=\$125\\\\Cost_2=(125+2*30)/(200)\\\\\\=0.925`

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=(C_(pc)+Wage)/(Items) \ , C_(pc)=\$125\\\\Cost_3=(125+3*30)/(220)\\\\\\=0.98`

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=(C_(pc)+Wage)/(Items) \ , C_(pc)=\$125\\\\Cost_4=(125+4*30)/(234)\\\\\\=1.05`

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.