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?

Answer 1

to calculate this we need to find derivative of C

C' = -40 + 0.5x = 0
x = 40/0.5 = 80

Every time you have a function that depends on some variable and you need to calculate minimum or maximum, make derivative of it and set it equal to 0