an aircraft factory manufactures airplane engines. the unit cost c (the cost in dollars to make each…

an aircraft factory manufactures airplane engines. the unit cost c (the cost in dollars to make each airplane engine) depends on the number of engines made. if x engines are made, then the unit cost is given by the function c(x)=0.3x² - 180x + 33,637. how many engines must be made to minimize the unit cost? do not round your answer. number of airplane engines:

an aircraft factory manufactures airplane engines. the unit cost c (the cost in dollars to make each airplane engine) depends on the number of engines made. if x engines are made, then the unit cost is given by the function c(x)=0.3x² - 180x + 33,637. how many engines must be made to minimize the unit cost? do not round your answer. number of airplane engines:

Answer

Explanation:

Step1: Identify quadratic - form coefficients

For a quadratic function $y = ax^{2}+bx + c$, in $C(x)=0.3x^{2}-180x + 33637$, $a = 0.3$, $b=-180$, $c = 33637$.

Step2: Use vertex - formula for minimum

The $x$ - value of the vertex of a quadratic function $y = ax^{2}+bx + c$ (where $a>0$, the function has a minimum) is given by $x=-\frac{b}{2a}$. Substitute $a = 0.3$ and $b=-180$ into the formula: $x=-\frac{-180}{2\times0.3}$.

Step3: Calculate the value of $x$

$x=\frac{180}{0.6}=300$.

Answer:

300