Solve the problem.
-The cost in millions of dollars for a company to manufacture x thousand automobiles is given by the function $$C ( x ) = 4 x ^ { 2 } - 32 x + 128$$ Find the number of automobiles that must be produced to minimize the cost.
A)64 thousand automobiles
B)16 thousand automobiles
C)8 thousand automobiles
D)4 thousand automobiles

Question

Quizplus · Accepted Answer

The cost function is a quadratic function in the form $C(x) = ax^2 + bx + c$. The minimum cost occurs at the vertex of the parabola, which is given by $x = -\frac{b}{2a}$. Here, $a = 4$ and $b = -32$, so $x = -\frac{-32}{2 \times 4} = 4$. Thus, 4 thousand automobiles must be produced to minimize the cost.

Solve the Problem C(x)=4x2−32x+128C ( x ) = 4 x ^ { 2 } - 32 x + 128C(x)=4x2−32x+128

Solve the Problem $C ( x ) = 4 x ^ { 2 } - 32 x + 128$