Answer
(a) 63 clubs
(b) 151.9 dollars
Work Step by Step
Since its an upward-facing quadratic, the minimal marginal cost is the global minimum, which in this case is represented by the vertex's y-value. Thus, let's re-write the quadratic equation to vertex form:
$C(x)=4.9x^2-617.4x+19,600$
$C(x)=4.9(x^2-126x)+19,600$
$C(x)=4.9(x^2-126x+(\frac{126}{2})^2)+19,600-4.9(\frac{126}{2})^2$
$C(x)=4.9(x^2-126x+63^2)+19,600-4.9(3969)$
$C(x)=4.9(x-63)^2+19,600-19,448.1$
$C(x)=4.9(x-63)^2+151.9$
So, the number of clubs (x) where the marginal cost is lowest is represented by the x-value of the vertex which is 63 clubs. The minimum marginal cost is represented by the y-value of the vertex which is 151.9 dollars.
