Imagine you have some workers and some handheld computers that you can use to ta

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 200 items per hour. And four or more workers sharing a computer can together inventory fewer than 210 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? What is the cost of inventorying a single item?

What if you assign three workers per computer?

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

Explanation / Answer

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 200 items per hour. And four or more workers sharing a computer can together inventory fewer than 210 items per hour.

Computers cost $100 each and you must pay each worker $25 per hour.

If you assign one worker per computer, then total cost is $100 + $25 = $125. Now in this time, total itmes inventoried = 100. Hence cost of inventorying a single item is 125/100 = $1.25

If you assign two workers per computer, then total cost is $100 + $25*2 = $150. Now in this time, total itmes inventoried = 150. Hence cost of inventorying a single item is 150/150 = $1

If you assign three workers per computer, then total cost is $100 + $25*3 = $175. Now in this time, total itmes inventoried = 200. Hence cost of inventorying a single item is 175/200 = $0.875

If you assign four workers per computer, then total cost is $100 + $25*4 = $200. Now in this time, total itmes inventoried = less than 210. Hence cost of inventorying a single item is 200/210 = $0.95

Hence there should be threeworkers per computer should you assign if you wish to minimize the cost of inventorying a single item which is then minimized at $0,875.

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