For the given cost function Cx 62500 400x x2 find The pro

For the given cost function C(x) = 62500 + 400x + x^2 find: The production level that will minimize the average cost The minimal average cost

Solution

given cost C(x)=62500+400x +x²

average cost AC(x) =(C(x))_/x

average cost AC(x) =(62500+400x +x²)_/x

average cost AC(x) =(62500_/x)+400 +x

a)AC\'(x)=(-62500_/x²)+0 +1

AC\'(x)=(-62500_/x²) +1

AC\'\'(x)=(125000_/x³)

for minimum average cost AC\'(x)=0,AC\'\'(x)>0

(-62500_/x²) +1=0

(62500_/x²) =1

x²=62500

x =250

AC\'\'(250)=(125000_/250³)>0

production level that will minimise the average cost =250

b) minimal average cost AC(250) =(62500_/250)+400 +250

minimal average cost =250+400 +250

minimal average cost =900