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)=0.5x² - 230x + 36,688. 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)=0.5x² - 230x + 36,688. how many engines must be made to minimize the unit cost? do not round your answer. number of airplane engines:

Answer

Explanation:

Step1: Identify the function type

The cost function $C(x)=0.5x^{2}-230x + 36688$ is a quadratic function in the form $y = ax^{2}+bx + c$, where $a = 0.5$, $b=-230$, $c = 36688$.

Step2: Recall the formula for the vertex of a quadratic

For a quadratic function $y = ax^{2}+bx + c$, the x - coordinate of the vertex (which gives the minimum or maximum value) is $x=-\frac{b}{2a}$.

Step3: Calculate the value of x

Substitute $a = 0.5$ and $b=-230$ into the formula $x =-\frac{b}{2a}$. $x=-\frac{-230}{2\times0.5}=\frac{230}{1}=230$.

Answer:

230