a)
In order to find the number of players that should be produced to minimize the marginal cost, we just need to calculate the x-coordinate of the quadratic equation vertex.
This vertex represents the minimum point of the function (the point with the smallest value of y).
So, to find the vertex x-coordinate, we can use the following formula, after comparing the function with the standard form:
Therefore 50 players should be produced to minimize the marginal cost.
b)
To calculate the minimum marginal cost, let's use the number of players found in item a in the equation for the marginal cost:
Therefore the minimum marginal cost is $4,900.