Question

A) Find the marginal cost function.B) Find the marginal cost at x = 100.(c) Find the cost at x = 100.

Answer 1

a) The marginal cost is given by the derivative of the function C(x). Therefore:

$\begin{gathered} C^{\prime}(x)=3+2(0.01)x+3(0.0002)x^2 \\ C^{\prime}(x)=3+0.02x+0.0006x^2 \end{gathered}$

Answer a:

$C^{\prime}(x)=3+0.2x+0.0006x^2$

b) The marginal cost at x = 100 is:

$\begin{gathered} C^{\prime}(x)=3+0.2(100)+0.0006(100)^2 \\ C^{\prime}(x)=3+20+6=29 \end{gathered}$

Answer b: $29

c) The cost at x = 100 is:

$\begin{gathered} C(x)=4900+3(100)+0.01(100)^2+0.0002(100)^3 \\ C(x)=4900+300+100+200 \\ C(x)=5500 \end{gathered}$

Answer c: $5500