The total cost of producing a type of car is given by C (x) = 12000-40x+0.04x2, where x is the number of cars produced. How many cars should be produced to incur minimum cost?

Step-by-step explanation:

C' (x) = -40+0.08 x

C' (x) = 0 gives

-40+0.08 x=0

x=40/0.08=500

C" (x) = 0.08>0 at x=500

so C (x) is minimum if x=500

so 500 cars need to be produced for minimum cost.

or we can solve by completing the squares.

c (x) = 12000+0.04 (x²-1000 x+250000-250000)

=12000+0.04 (x-500) ²-0.04*250000

=0.04 (x-500) ²+12000-10000

=0.04 (x-500) ²+2000

c (x) is minimum if x=500