The cost function for production of a commodity is C(x)=339+25x-0.09x^{2}+0.0004x^{3} Compare C’(100)

Paganellash

Paganellash

Answered question

2021-12-04

The following is the cost function for producing a commodity:
C(x)=339+25x0.09x2+0.0004x3 
Compare C’(100) with the cost of producing the 101st item.

Answer & Explanation

Coon2000

Coon2000

Beginner2021-12-05Added 15 answers

C(x)=339+25x0.09x2+0.0004x3
C(x)=250.18x+0.0012x2 (marginal cost)
Increase in cost as x=100 units
C'(100)=19
Cost of 101st item:
C(101)C(100)2358.03233919.03
C'(100) is roughly equal to the increase in production costs for the 101st item.
Result:
C'(100) is approximately the same as the increase in cost to produce the 101st item.

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