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 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?

Explanation / Answer

For one computer and one worker, the cost to inventory 1 item will be the cost of the computer + the cost of the worker=125/100 items perhour=1.25 items inventoried by one computer and one worker. For two workers and one computer, the cost would now be 100+25+25=150/150 items per hour= 1 item inventoried. For three we compute the same way 100+25+25+25=175/160 items=1.09 items if we wish to minimmize cost we want to assign the number of workers to a computer where the change in inventory is 0. Notice, 1 worker=100 items 2 workers=150 items 3 workers=160 items 4+ workers=160 items Therefore, we stop at three workers per computer because we dont want to py the labor cost for the same output produce. In this case, there would be excess labor and not enough capital. In other words, there will be people sitting around with no computer to use. So again, our final answer is 3 workers per computer. Hope this helps

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