Solve the problem.
-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) 6 thousand automobiles
C) 36 thousand automobiles
D) 15 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 $b = -30$. Thus, the x-coordinate is $-\frac{-30}{2*5} = 3$. Therefore, the number of automobiles that must be produced to minimize the cost is 3 thousand.

Solve the Problem xxx Thousand Automobiles Is Given by the Function C(x)=5x2−30x+81C ( x ) = 5 x ^ { 2 } - 30 x + 81C(x)=5x2−30x+81

Solve the Problem $x$ Thousand Automobiles Is Given by the Function $C ( x ) = 5 x ^ { 2 } - 30 x + 81$