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)=1.1x² - 330x + 43,468. what is the minimum unit cost? do not round your answer. unit cost: $

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)=1.1x² - 330x + 43,468. what is the minimum unit cost? do not round your answer. unit cost: $

Answer

Explanation:

Step1: Identify the function type

The cost function $C(x)=1.1x^{2}-33x + 43.468$ is a quadratic function in the form $y = ax^{2}+bx + c$, where $a = 1.1$, $b=-33$, and $c = 43.468$. Since $a>0$, the parabola opens upward and the vertex of the parabola gives the minimum - value of the function.

Step2: Find the x - coordinate of the vertex

The x - coordinate of the vertex of a quadratic function $y = ax^{2}+bx + c$ is given by $x=-\frac{b}{2a}$. Substitute $a = 1.1$ and $b=-33$ into the formula: $x=-\frac{-33}{2\times1.1}=\frac{33}{2.2}=15$.

Step3: Find the minimum cost

Substitute $x = 15$ into the cost function $C(x)=1.1x^{2}-33x + 43.468$: $C(15)=1.1\times(15)^{2}-33\times15 + 43.468$ $=1.1\times225-495 + 43.468$ $=247.5-495 + 43.468$ $=-247.5+43.468$ $=-204.032$.

Answer:

$-204.032$