Solve.
-The cost in millions of dollars for a company to manufacture $x$ thousand automobiles is given by the function $C ( x ) = 5 x ^ { 2 } - 30 x + 81$. Find the number of automobiles that must be produced to minimize the cost.
A) 3 thousand automobiles
B) 36 thousand automobiles
C) 15 thousand automobiles
D) 6 thousand automobiles

Question

Quizplus · Accepted Answer

The cost function $C(x) = 5x^2 - 30x + 81$ is a quadratic function, where the coefficient of $x^2$ is positive, indicating a parabola that opens upwards. The minimum cost occurs at the vertex of the parabola. The x-coordinate of the vertex can be found using the formula $-\frac{b}{2a}$, where $a = 5$ and $b = -30$. Substituting these values gives $-\frac{-30}{2*5} = 3$, meaning the minimum cost occurs when 3 thousand automobiles are produced.

Solve -The Cost in Millions of Dollars for a Company xxx

Solve
-The Cost in Millions of Dollars for a Company $x$