Differential Equations Question 282
Question: The marginal cost of manufacturing a certain item is given by $ c’(x)=\frac{dc}{dx}=2+0.15x $ . The total cost function c (x), is
Options:
A) $ 0.075x^{2}+2x+100 $
B) $ 0.15x^{2}+3x+30 $
C) $ x^{2}+100.075x+100 $
D) None of these It is given that c (0) = 100
Show Answer
Answer:
Correct Answer: A
Solution:
[a] [Note derivative of a function is sometimes called as the marginal value, especially in economics] Given $ \frac{dc}{dx}=2+0.15x $ Integrating we get $ c(x)=2x+0.15\frac{x^{2}}{2}+D $ when $ x=0,c(x)=100\Rightarrow D=100 $
$ \therefore $ the required equation is $ c(x)=0.075x^{2}+2x+100 $
BETA
