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 250 items per hour. And four or more workers sharing a computer can together inventory fewer than 260 items per hour. Computers cost $125 each and you must pay each worker $30 per hour. Instructions: Round your answers to 2 decimal places. 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.

Answer 1

(a)

One worker per computer can inventory 150 items per hour.

Cost of computer = 125

Wage of one worker = 30

Total cost of employing one worker per computer = 125 + 30 = 155

Cost of inventorying a single item = Total cost/Total output = 155/150 = 1.03

The cost of inventorying a single item is $1.03

(b)

Two workers per computer can inventory 200 items per hour.

Computer cost = $125

Wage paid to two workers = 30 * 2 = 60

Total cost of employing 2 workers per computer = 125 + 60 = 185

Cost of inventorying single item = Total cost/Total output = 185/200 = $0.92

The cost of inventorying single item is $0.92

(c)

Three workers per computer can inventory 250 items per hour.

Computer cost = 125

Wages paid to three workers = 30 * 3 = 90

Total cost of employing 3 workers per coputer = 125 + 90 = 215

Cost of inventorying single item = Total cost/Total output = 215/250 = $0.86

The cost of inventorying single item is $0.86

(d)

3 workers should be assigned per computer in order to minimize the cost of inventorying a single item.