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)=0.9x² - 558x + 95,003. 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)=0.9x² - 558x + 95,003. 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 $C(x)=0.9x^{2}-558x + 95003$ is a quadratic function in the form $y = ax^{2}+bx + c$, where $a = 0.9$, $b=-558$, and $c = 95003$.

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 for $a>0$) is $x=-\frac{b}{2a}$.

Step3: Substitute the values of $a$ and $b$ into the formula

Substitute $a = 0.9$ and $b=-558$ into $x=-\frac{b}{2a}$. We get $x=-\frac{-558}{2\times0.9}$.

Step4: Calculate the value of $x$

First, simplify the denominator: $2\times0.9 = 1.8$. Then, $x=\frac{558}{1.8}=310$.

Answer:

310