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Assume that General Dynamics, which manufactures high-technology instruments for spacecraft, is considering the sale of a navigational unit to a government agency in India that wishes to launch its own communications satellite. The government agency plans to purchase 8 units, although it would also consider buying 16 units. General Dynamics has started a chart relating labor time required to units produced.
Unit produced Time Required to Unit Produced (X) Produce the Xth Unit
1 10,000 hours
2 8,000 hours
4 6,400 hours
8 ?
16 ?
a. Compute the labor time required to produce 8 and 16 units.
b. Assume that labor time costs $125 per hour. Compare the cost of producing the 1st unit to the cost of producing the 16th unit. What is the percentage of the cost of the 16th unit to the cost of the 1st unit?

Respuesta :

TomShelby

Answer:

labor hour  of the 8th units: 5,120

of the 16th units: 4,096

cost difference between the first and last: 738,000

the 16th is made with 40.96% o the cost of the 1st unit.

Explanation:

We calculate the learning efficiency rate which is the time saved once production is doubled:

8,000 / 10,000 = 0.8

6,400 / 8,000 = 0.8

The rate is 80% thus we multiply the 4th unit by 80% to get the 8th units labor hours:

6,400 x 0.8 = 5,120

Then, it will also double at the 16th units so we repreat the process:

5,120 x 0.8 = 4.096‬

first unit labor cost: 10,000 x $125 =  1,250,000

16th unit labor cost: 4,096 x $125 =     512,000  

difference:                                              738,000

percentage: 512,000 / 1,250,000  = 0,4096‬ = 40.96%