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 100 items per hour. Two workers sharing a computer can together inventory 150 items per hour. Three workers sharing a computer can together inventory 160 items per hour. And four or more workers sharing a computer can together inventory fewer than 160 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? What if you assign two workers per computer? Three? How many workers per computer should you assign if you wish to minimize the cost of inventorying a single item?

Answer 1

Step-by-step explanation:

Given:

computer sharing:

1 worker

inventory 100 items per hour

2 workers

inventory 150 items per hour

3 workers

Inventory 160 items per hour

Cost:

computer = $100

Workers = $25

Total cost for inventorying a single item, T:

1 worker makes an inventory of 100 items per hour

T1 = (100 + 25)/100

= 125/100

= $1.25/item

2 workers makes an inventory of 150 items

T2 = (100 + 2 × (25))/150

= (100 + 50)/150

= $1/item

3 workers can make an inventory of 160 items

T3 = (100 + 3 × (25))/160

= (100 + 75)/160

= 175/160

= $1.09/item

Since the minimum cost of inventorying a single item from the above is $1/item.

To minimise the cost of inventorying a single item you assign 2 workers per computer.