Solution
The cost function of producing x coffee machines is
[tex]C(x)=2100+50x-0.1x^2[/tex](A). Find the exact cost of producing the 21st machine
First, The cost of producing the first 21 coffee machines is given by
[tex]\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}[/tex]Secondly, the cost of producing the first 20 coffee machines is given by
[tex]\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}[/tex]Thus, the exact cost of producing the 21st machine is
[tex]\begin{gathered} C(21)-C(20)=3105.9-3060 \\ C(21)-C(20)=45.9 \end{gathered}[/tex]Therefore, the cost of producing the 21st machine is $45.9
