In a perfectly competitive industry, the market price is $30. A firm is currently producing 10,000 units of output, its average total cost is $35, its marginal cost is $25, and its average variable cost is $25. Given these facts, explain whether the following statement are true or false.

a. The firm is currently producing at the minimum average variable cost

b. The firm should produce more output to maximize its profit

c. Average total cost will be less than $35 at the level of output that maximizes the firm's profit.

Explain your response to each part.

(Assume normal U-shaped cost curve for this problem)