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 - 330x + 61,463. 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 - 330x + 61,463. 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 $C(x)=0.5x^{2}-330x + 61463$ is a quadratic function in the form $y = ax^{2}+bx + c$, where $a = 0.5$, $b=-330$, $c = 61463$.

Step2: Recall the formula for the vertex of a quadratic function

For a quadratic function $y = ax^{2}+bx + c$, the x - coordinate of the vertex (which gives the minimum value when $a>0$) is $x=-\frac{b}{2a}$.

Step3: Substitute the values of a and b

Substitute $a = 0.5$ and $b=-330$ into the formula $x=-\frac{b}{2a}$. We have $x=-\frac{-330}{2\times0.5}$.

Step4: Calculate the value of x

First, simplify the denominator: $2\times0.5 = 1$. Then, $x=\frac{330}{1}=330$.

Answer:

330