Question

In: Statistics and Probability

Samsung manufactures cellular phones at a processing cost of $203 per unit. Currently, the company produces...

Samsung manufactures cellular phones at a processing cost of $203 per unit.

Currently, the company produces an average of 2002 phones per day, 85 percent of which are good-quality phones, resulting in 15 percent defective phones, 62 percent of which can be reworked. The cost of reworking a defective phone is $73.

They also consider a quality improvement initiative: They can replace a plastic component with a metal one which increases the initial cost of processing phone to $211, but the percentage of defective items decreases to 11 percent. With this quality improvement option, nothing else would be different from the current situation (for example the cost of rework and the percentage of defectives that can be reworked stay the same).

Calculate the followings:

Number of units reworked daily with current situation
Daily product yield with current situation
Effective production cost per unit with current situation
With the current situation, if the company wants the yield to be 2000, how many phones they should process daily?
Number of units reworked daily with suggested quality improvement option
Daily product yield with suggested quality improvement option
Effective production cost per with suggested quality improvement option
Should Samsung should take the suggested quality improvement initiative?
1. Yes
2. No

Expert Solution

the company produces an average of 2002 phones per day

85 percent of which are good-quality phones = 2002 (85/100) = 1701.7 ~ 1702 phones

resulting in 15 percent defective phones = 2002 (15/100) = 300.3 ~ 300 phones

62 percent of which can be reworked = 300 (62/100) = 186 phones

Number of units reworked daily with current situation 186 units

Daily product yield with current situation = 1702 + 186 = 1888 units

the initial cost of processing phone to $211

the company produces an average of 2002 phones per day

sub total cost = 211 × 2002 = $422422

The cost of reworking a defective phone is $73.

Number of units reworked daily with current situation 186 units

total cost of reworking a defective phones = 186 × 73 = $13578

Total production cost = 422422 + 13578 = 436000

Effective production cost per unit with current situation = 436000/2002 = $217.78

let X be the number of phones

if the company wants the yield to be 2000, how many phones they should process daily i.e

X(85/100)+X(15/100)(62/100) = 2000

0.85X+0.093X = 2000

X = 2120.89 ~ 2121

if the company wants the yield to be 2000, 2121 phones they should process daily.

Number of units reworked with quality improvement option = 2121(15/100)(62/100) = 197.253 ~ 197

Daily product yield= 2121(85/100) + 197 = 1803 + 197 = 2000

the initial cost of processing phone to $211

the company produces an average of 2121 phones per day

sub total cost = 211 × 2121 = $447531

The cost of reworking a defective phone is $73.

Number of units reworked daily with current situation 186 units

total cost of reworking a defective phones = 186 × 73 = $13578

Total production cost = 447531 + 13578 = $461109

Effective production cost per unit with current situation = 461109/2121 = $217.40

YES, Because Samsung should take the suggested quality improvement initiative as there is decrease in the effective production cost per unit with no change in the percentage of defective phones.

orchestra answered 2 years ago

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