Suppose you are a perfectly competitive firm producing computer memory chips. Your production capacity is 1000 units per year. Your marginal cost is $10 per chip up to capacity. You have a fixed cost of $10,000 if production is positive and $0 if you shut down. What are your profit-maximizing levels of production and profit if the market price is
(a) $5 per chip,
(b) $15 per chip, and
(c) $25 per chip? For case (b), explain why production is positive even though profits are negative.