Question

The total cost (in dollars) of producing a coffee machines is C(x) = 2100 + 50x - 0.1x^2.(A) Find the exact cost of producing the 21st machine.Exact cost of 21st machine= __(B) Use marginal cost to approximate the cost of producing the 21st machine.Approx. cost of 21st machine =

Answer 1

we know that

the function of the cost is equal to

`C(x)=2,100+50x-0.1x^2`

Part A

For x=21 machine

substitute in the function above

`C(21)=2,100+50(21)-0.1(21)^2`

C(21)=$3,105.90

therefore

The exact cost of 21st machine=$3,105.90

Part B

Use marginal cost to approximate the cost of producing the 21st machine

Remember that

The marginal cost function is the derivative of the total cost function, C(x)

so

Find out the first derivative of the function C(x)

`C^(\prime)(x)=50-0.2x`

For x=21

substitute

`\begin{gathered} C^(\prime)(21)=50-0.2(21) \\ C^(\prime)(21)=\$45.8 \end{gathered}`