The total cost function is given as:

C(q)=4000+50q+0.002q2C(q)=4000+50q+0.002q2

The average cost function is:

AC(q)=C(q)qAC(q)=4000q+50+0.002qAC(q)=C(q)qAC(q)=4000q+50+0.002q

Minimizing the average cost function, we get:

ΔC(q)Δq=0−4000q2+0.002=0−4000+0.002q2=00.002q2=4000q2=2000000q=√2000000q≈1,414.21unitsΔC(q)Δq=0−4000q2+0.002=0−4000+0.002q2=00.002q2=4000q2=2000000q=2000000q≈1,414.21units

The average cost is at its minimum at q≈1,414.21unitsq≈1,414.21units

The Average Total Cost:

The average cost is equal to the total cost divide by the total output. The shape of the average cost is U-shaped, meaning that it starts by decreasing as more output is produced, reaches the minimum point, and then starts to increase as more and more output is produced.