Solve.
-The cost in millions of dollars for a company to manufacture $x$ thousand automobiles is given by the function $C ( x ) = 4 x ^ { 2 } - 40 x + 200$. Find the number of automobiles that must be produced to minimize the cost.
A) 5 thousand automobiles
B) 10 thousand automobiles
C) 20 thousand automobiles
D) 100 thousand automobiles

Question

Quizplus · Accepted Answer

The cost function $C(x) = 4x^2 - 40x + 200$ 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 $a = 4$ and $b = -40$. Thus, the x-coordinate is $-\frac{-40}{2*4} = \frac{40}{8} = 5$. Therefore, the number of automobiles that must be produced to minimize the cost is 5 thousand.

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

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