Expert: Paul Klarreich - 12/1/2008

Question
Carla Music Company estimates that the marginal cost of manufacturing its professional series guitar is C’ (x) = .002x + 100 dollars/month when the level of production is x guitars/month. The fixed costs by Carla are $4000 per month.

A. Find the total monthly cost incurred by Carla in manufacturing x guitars per month.

B. What is the cost of producing 50 guitars per month.


I am soo confused on this problem and I have no idea how to even start.  Can you please help me?!?

Answer
Questioner:   blaine
Category:  Calculus
Private:  No
 
Subject:  Calculus
Question:  Carla Music Company estimates that the marginal cost of manufacturing its professional series guitar is C’ (x) = .002x + 100 dollars/month when the level of production is x guitars/month. The fixed costs by Carla are $4000 per month.

A. Find the total monthly cost incurred by Carla in manufacturing x guitars per month.

B. What is the cost of producing 50 guitars per month.


I am soo confused on this problem and I have no idea how to even start.  Can you please help me?!?
..............................................
Hi, Blaine,

You start by stating what your terms mean, and what you want to find:

Marginal cost is  dC/dx

C(0) = 4000 [initial condition]

Find C(x)

If C'(x) = 0.002x + 100, then integrate this and use the initial condition.