Answer:
The minimum unit cost is $12,197.
Explanation:
The cost function is given below:
[tex]C\mleft(x\mright)=x^2-520x+79,797[/tex]To find the minimum unit cost, first, find the derivative of C(x).
[tex]C^{\prime}(x)=2x-520[/tex]Next, set the derivative equal to 0 and solve for x.
[tex]\begin{gathered} 2x-520=0 \\ 2x=520 \\ x=520\div2 \\ x=260 \end{gathered}[/tex]Finally, substitute x=260 into C(x) to find the minimum cost.
[tex]\begin{gathered} C\mleft(x\mright)=x^2-520x+79,797 \\ \implies C(260)=(260)^2-520(260)+79,797 \\ =67600-135,200+79,797 \\ =12,197 \end{gathered}[/tex]The minimum unit cost is $12,197.
