Homework SourseSuppose that the cost in dollars for a company to produce x
Suppose that the cost (in dollars) for a company to produce x pairs of a new line of jeans is given by
C(x)=2000+3x+0.01x^2 +0.0002x^3
a)find the marginal cost funtion
b)findC\'(100) and explain its meaning. What does it predict?
c)Calculate the cost of manufacturing the 101st through the 110th pair using only the marginal cost function.
show your work
C(x)=2000+3x+0.01x^2 +0.0002x^3
a)find the marginal cost funtion
b)findC\'(100) and explain its meaning. What does it predict?
c)Calculate the cost of manufacturing the 101st through the 110th pair using only the marginal cost function.
show your work
Solution
Marginal Cost is the differential of Total Cost Equation (assumed that it is differentiable)
solution:
a) Marginal Cost, MC(x) = C\'(x) = 3 + 0.02x + 0.0006x2
b) C\'(100) = 3 + 0.02(100) + 0.0006(100*100) = 11
It signifies and predicts the additional cost incurred in producing the next unit.
c) The required answer is the definite integral of MC(x) from 100 to 110.
The answer is 3(110-100) + 0.02(110-100) + 0.0006(1102-1002) which is equal to 31.46
