Imagine you have some workers and some handheld computers th

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 125 items per hour. Two workers sharing a computer can together inventory 175 items per hour. Three workers sharing a computer can together inventory 225 items per hour. And four or more workers sharing a computer can together inventory 235 items per hour. Computers cost $100 each and you must pay each worker $25 per hour.

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

Instructions: Round your answer to two decimal places.
   
$ _____ per item

If you assign two workers per computer, what is the cost of inventorying a single item?

Instructions: Round your answer to two decimal places.

$ _______ per item

If you assign three workers per computer, what is the cost of inventorying a single item?

Instructions: Round your answer to two decimal places.

$ _____ per item

Instructions: Round your answer to two decimal places.

If you assign four workers per computer, what is the cost of inventorying a single item?

$ _____ per item

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

_____ worker(s) per computer

Solution

(1) 1 worker per computer

Cost of computer = $100

Labor cost = $25

Total cost of inventory = $100 + $25 = $125

Therefore, Cost of a single item = $125 / 125 = $1

(2) 2 computers per worker

Cost of computer = $100

Labor cost = $25 x 2 = $50

Total cost of inventory = $100 + $50 = $150

Therefore, Cost of a single item = $150/175 = $0.857

(3) 3 workers per computer

Cost of computer = $100

Labor cost = $25 x 3 = $75

Total cost of inventory = $100 + $75 = $175

Therefore, Cost of a single item = $175 / 225 = $0.778

(4) 4 workers per computer

Cost of computer = $100

Labor cost = $25 x 4 = $100

Total cost of inventory = $100 + 100 = $200

Therefore, Cost of a single item = $200 / 235 = $0.851

(5) Minimum cost of single item is $0.778 when 3 workers share a computer. So, one should assign 3 workers for a computer.