Answer: no higher than $10, higher than $14, no higher than $10
Explanation:
In a perfectly (purely) competitive market, the long run equilibrium level of production of a firm corresponds to the point where the marginal cost is equal to the price and the minimum of the average total cost.
The fact that the firm continues to produce tells you that the average variable cost is no higher than $10 since that would lead the firm to shut down. When the price ceiling is imposed, the firm will reduce production to the point where its marginal cost is equal to the new price (no higher than $10). You also know that the long run level of production corresponds to the minimum value of the ATC curve. As a result, you know that the new level of production must correspond to a higher ATC. Since in the long run the average total cost equals the market price, you know that at this new level of production the average total cost is higher than $14.