Answer :
Answer:
Explanation:
We were given the following information:
[tex]C\left(x\right)=1.2x^2-504x+64558[/tex]We will take the first derivative of the function, we have:
[tex]\begin{gathered} C^{\prime}(x)=2(1.2x^{2-1})-504 \\ C^{\prime}(x)=2.4x-504 \\ \text{We equate the derivative to zero \lparen minimum cost\rparen:} \\ 2.4x-504=0 \\ \text{Add ''504'' to both sides, we have:} \\ 2.4x-504+504=504 \\ 2.4x=504 \\ \text{Divide both sides by ''2.4'', we have:} \\ x=\frac{504}{2.4} \\ x=210engines \end{gathered}[/tex]We will substitute this into the initial function to obtain the minimum cost. We have:
[tex]\begin{gathered} C(210)=1.2(210)^2-504(210)+64558 \\ C(210)=52920-105840+64558 \\ C(210)=11638 \\ C(210)=\text{\$11,638} \end{gathered}[/tex]Therefore, the minimum cost is $11,638
