Imagine you have some workers and some hand-held 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 can together inventory 150 items per hour. Three workers can together inventory 160 items per hour. And four or more workers 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?

Explanation:

The computation is shown below:

a. For one computer, the cost of inventorying a single item is

= Total cost ÷ Number of inventory items

where,

total cost is $100 + $25 = $125

And, the number of inventory items is 100

So, the cost of inventorying a single item is

= $125 ÷ 100 items

= $1.25

b. Now for two workers, it is

= Total cost ÷ Number of inventory items

where,

total cost is $100 + $25 + $25 = $125

And, the number of inventory items is 150

So, the cost of inventorying a single item is

= $150 ÷ 150 items

= $1

For three, it would be

= Total cost ÷ Number of inventory items

where,

total cost is $100 + $25 + $25 + $25 = $175

And, the number of inventory items is 160

So, the cost of inventorying a single item is

= $175 ÷ 160 items

= $1.09375

So we can choose the two workers for minimizing the cost

answer; synthetic production system;