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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

For the given cost function C(x) = 16900 + 400x + x^2, find:

a) The cost at the production level 1400
b) The average cost at the production level 1400
c) The marginal cost at the production level 1400
d) The production level that will minimize the average cost
e) The minimal average cost

Learn how to analyze a cost function with the example C(x) = 16900 + 400x + x^2. This includes calculating cost, average cost, marginal cost, and finding the production level that minimizes average cost. Suitable for undergraduate students studying economics or business.

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