Question

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

Answer 1

The cost function of producing x coffee machines is

`C(x)=2100+50x-0.1x^2`

(A). Find the exact cost of producing the 21st machine

First, The cost of producing the first 21 coffee machines is given by

`\begin{gathered} C(x)=2100+50x-0.1x^2 \\ C(21)=2100+50(21)-0.1(21)^2 \\ C(21)=2100+1050-44.1 \\ C(21)=3105.9 \end{gathered}`

Secondly, the cost of producing the first 20 coffee machines is given by

`\begin{gathered} C(x)=2100+50x-0.1x^2 \\ C(20)=2100+50(20)-0.1(20)^2 \\ C(20)=2100+1000-40 \\ C(20)=3060 \end{gathered}`

Thus, the exact cost of producing the 21st machine is

`\begin{gathered} C(21)-C(20)=3105.9-3060 \\ C(21)-C(20)=45.9 \end{gathered}`

Therefore, the cost of producing the 21st machine is $45.9