Question

If TC=0.01x²+5x+100 is the cost function for x items of a product, at what level of production, x is there minimum average cost? What is the minimum average cost?

Answer 1

$T_c(x)=0.01x^2+5x+100\\T'(x)=0.02x+5\\$

At optimal point: $T'_c(x_0)=0$

$0.02x_0+5=0\\0.02x_0=-5\\x_0=-\frac{5}{0.02}$

$x_0=-25<0$

$x_0=0$

$T_c(x_0)=0+0+0+100$

therefore, the minimum average cost is 100