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Ad libitum [116K]
3 years ago
8

Imagine you have some workers and some handheld computers that you can use to take inventory at a warehouse. There are diminishi

ng 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 $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?
Mathematics
1 answer:
Svet_ta [14]3 years ago
4 0

Answer:

a. $1.03

b. $0.93

c. 0.98

d. 2 workers

Step-by-step explanation:

a. Given that:

  • 1 computer : 1 worker : inventory 150 items per hour
  • 1 computer : 2 workers : inventory 200 items per hour
  • 1 computer : 3 workers : inventory 220 items per hour
  • 1 computer : 4+ workers : fewer than 235 items per hour
  • Cost: $100 per computer ; $25 per worker

The fixed production factor in the warehouse is the computer used:

-One computer used, but the number of users is varied to inventory a specified number of items.

-The variable production factor is the number of workers assigned per one computer.

#The cost of inventorying a single item by one worker is:

Cost=\frac{C_{pc}+Wage}{Items} \ , C_{pc}=\$125\\\\Cost_1=\frac{125+30}{150}\\\\\\=1.03

Hence, the cost of inventorying a single item is $1.03

b. Using the information provided above, the cost of inventorying a single item when two workers are assigned is :

Cost=\frac{C_{pc}+Wage}{Items} \ , C_{pc}=\$125\\\\Cost_2=\frac{125+2\times30}{200}\\\\\\=0.925

Hence, the cost of inventorying a single item is $0.93

c.Using the information provided above, the cost of inventorying a single item when three workers are assigned is :

Cost=\frac{C_{pc}+Wage}{Items} \ , C_{pc}=\$125\\\\Cost_3=\frac{125+3\times30}{220}\\\\\\=0.98

Hence, the cost of inventorying a single item is $0.98

d. To determine the most cost-effective job assignment, we calculate the cost of 4+ workers.

Take any number less than 235(say 234) as the inventory units:

Cost=\frac{C_{pc}+Wage}{Items} \ , C_{pc}=\$125\\\\Cost_4=\frac{125+4\times30}{234}\\\\\\=1.05

From our calculations, it's clear that two workers per computer costs the least amount($0.93) per unit item. Hence, it is best to assign two workers per computer.

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4n2-5n-6  

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Step  2  :

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Step-5 : Add up the four terms of step 4 :

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