Please answer all parts

3. (25 points) A firm can produce output using two inputs and the following production technology: q =xx; . The firm is a price-taker in both the markets where it buys its inputs and the one where it sells its output. The price of output is equal to $9 and the prices of both inputs are equal to $1. a) Find the firm's profit as a function of the input quantities. b) Find the profit-maximizing quantities of the inputs and the quantity of output that is produced. c) Verify that what you found is a unique global maximum