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 220 items per hour. And four or more workers sharing a computer can together inventory fewer than 235 items per hour. Computers cost $100 each and you must pay each worker $25 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.

Number of worker(s) per computer?

Answer 1

Answer : a) According to the given informations, per computer cost = $100 and per worker cost = $25

This means in case of one worker for one computer, the total cost = 100 + 25 = $125.

In case of one worker for one computer, the worker is inventoring 150 items per hour

Therefore, 150 items cost is $125

Now 1 item cost = 125 / 150 = $0.83

So, in case of one worker for one computer, the inventory cost for a single item is $0.83 .

b) Two worker's payment becomes = 25 * 2 = $50     [As one worker's payment is $25]

Total cost for two workers per computer = 100 + 50 = $150 [As per computer cost = $100]

200 items per hour are inventoring by two workers per computer with cost of $150

Now, 1 item cost = 150 / 200 = $0.75

Therefore, in case of two workers per computer , the cost of single item is $0.75 .

c) Payment of three workers = 3 * 25 = $75

Total cost of three workers per computer = 100 + 75 = $175 [As cost of one computer = $100]

220 items are inventoring by three workers per computer with cost of $175

Now, 1 item cost = 175 / 220 = $ 0.79

Therefore, in case of three workers per computer, the cost of single item is $0.79 .

d) Payment of four workers = 4 * 25 = $100

Total cost for three workers per computer = 100 + 100 = $200 [As one computer cost = $100]

235 items are inventoring by four or more workers per computer with cost of $200

Now, 1 item cost = 200 / 235 = $ 0.85

Therefore, in case of four or more workers per computer, the cost of single item is $0.85 .

By comparing the above discussion, it is  clear to us that in case of two workers per computer the cost of single item is lowest which is $0.75 in comparison to others.

So, to minimise the cost of single item's inventory 2 workers per computer should assign.