3. (35 points) A firm has a production function given by f($1, 12) = ]1;, where I] and I2 are the two inputs used to produce output y. Let the price the firm pays per unit of input 1 be wi, and the price the firm pays per unit of input 2 be w2. The firm is planning to produce y units of output.Short-run profit-maximization: In the short-run, the firm uses a2 units of input 2 and is unable to vary this quantity. In the short-run, the only thing that is left for the firm to choose is the amount of input 1. Let the price of the firm's output be p, and, once again, let the price the firm pays per unit of input 1 be wi, and the price the firm pays per unit of input 2 be w2. (c) Derive the firm's short-run demand function for input 1 and its short-run supply function. (d) Explain what happens to the short-run profit-maximizing production plan as the output price p decreases. Present graphically the short-run demand function for input 1 and show on the graph what happens to the quantity demanded when p decreases. (e) Given than w1 = w2 = $1, p = $9 and 12 = 27, find the firm's optimal level for input 1 and its optimal short-run output level. Calculate the firm's maximum short-run profit level