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 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 $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?

Instructions: Enter your answer as a whole number.

( ) worker(s) per computer.

Solution

(a) When one worker is assigned,

Total cost ($) = 125 + 1 x 30 = 125 + 30 = 155

Cost per item = $155/100 = $1.55

(b) When two workers are assigned,

Total cost ($) = 125 + 2 x 30 = 125 + 60 = 185

Cost per item = $185/150 = $1.23

(c) When three workers are assigned,

Total cost ($) = 125 + 3 x 30 = 125 + 90 = 215

Cost per item = $215/160 = $1.34

(d) Hiring four or more workers leads to negative marginal productivity, since number of items is less than 160. So,

Cost is minimized for hiring 2 workers per computer.