2 10 points If it costs approximately 500 1000 dollars to pr

2. (10 points) If it costs approximately 500 1000- dollars to produce z CD\'s. Use marginal analysis to approximate the cost of producing the 20th CD. Compare yo ur approximation with the actual cost of producing the 20th CD.

Solution

C = 1000 - 500/x

Deriving :
C\' or marginal cost C\'(x) = 500/x^2

So, cost to produce the 20th CD is approx :
C(20) - C(19) = C\'(20)

C(20) - C(19) = 500/(20)^2 = 1.25

So, cost to produce the 20th CD is
approx 1.25 dollars ----> ANS

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Actual cost :
C(20) = 100 - 500/20 = 75 ---> cost of producing 20 cd\'s

C(19) = 100 - 500/19 = 73.6842105263157895 --> cost of producing 19

So, subtracting :
C(20) - C(19) comes out to be :

75 - 73.6842105263157895

1.32 dollars approx