A manufacturer of lighting fixtures has daily production costs of
C = 800 − 40x + 0.25x2,
where C is the total cost (in dollars) and x is the number of units produced. How many fixtures should be produced each day to yield a minimum cost?

Question

A manufacturer of lighting fixtures has daily production costs of
C = 800 − 40x + 0.25x2,
where C is the total cost (in dollars) and x is the number of units produced. How many fixtures should be produced each day to yield a minimum cost?

anonymous · Answer

Minimum of a quadratic equation that opens up (note that the coefficient of x^2 is positive) is at x=-b/2a.  From this function a=1/4, b=-40, c=800.  So the minimum occurs at $$x=-b/2a=40/(2(1/4))=80$$