The total cost of producing a type of car is given by C(x)=23000−50x+0.2x2, where x is the number of cars produced. How many cars should be produced to incur minimum cost?

Answer 1

You need to find the value of x that minimizes the cost function.

c(x) = 2300-50x+0.2x²

The minimum is at the point where slope is 0. The slope is the first derivative of c(x) with respect to x.

d c(x) / dx = -50+0.4x (derivative of constant 2300 is 0. derivative of -50x is -50. Derivative of 0.2x² is 0.2*2*x)

Set the slope to 0,

-50+0.4x = 0

0.4x = 50

x = 125