Here are the answers for each part:

Given cost function: $C(x) = 16900 + 400x + x^2$

a) Cost at production level 1400

$C(1400) = 16900 + 400 \times 1400 + 1400^2 = 2393000$

b) Average cost at production level 1400

$\text{Average Cost} = \frac{C(x)}{x}$ $\text{Average Cost at } x = 1400 = \frac{2393000}{1400} = 1709.2857 \approx 1709.29$

c) Marginal cost at production level 1400

The marginal cost is the derivative of $C(x)$: $C'(x) = 400 + 2x$ $C'(1400) = 400 + 2 \times 1400 = 3200$

d) Production level that minimizes average cost

To minimize the average cost, set $C'(x) = \frac{C(x)}{x}$ and solve: $x = 200$

e) Minimal average cost