Question

(a) Find the marginal cost function.Answer:(b) Find the marginal cost at 2 = 100.Answer:(c) Find the cost at x = 100Answer:

Answer 1

We have the cost function for x units as:

`C(x)=7700+4x+0.01x^2+0.0002x^3`

a) We can find the marginal cost as the first derivative of the cost function:

`\begin{gathered} (dC)/(dx)=7700(0)+4(1)+0.01(2x)+0.0002(3x^2) \\ (dC)/(dx)=4+0.02x+0.0006x^2 \end{gathered}`

b) We can find the marginal cost when x = 100 by replacing x with 100 in the marginal cost function:

`\begin{gathered} (dC)/(dx)(100)=4+0.02(100)+0.0006(100^2) \\ (dC)/(dx)(100)=4+2+0.0006\cdot10000 \\ (dC)/(dx)(100)=4+2+6 \\ (dC)/(dx)(100)=12 \end{gathered}`

c) To calculate the cost at x = 100, we replace x with 100 in the cost function and calculate:

`\begin{gathered} C(100)=7700+4(100)+0.01(100^2)+0.0002(100^3) \\ C(100)=7700+400+0.01\cdot10000+0.0002\cdot1000000 \\ C(100)=7700+400+100+200 \\ C(100)=8400 \end{gathered}`

Answer:

a) 4 + 0.02x + 0.0006x²

b) 12

c) 8400