Please help with this Macro Theory question

1. Consider the following version of the firms profit maximization problem: The technology is y = f(X1, X2) where f (X1, X2) is (a) constant returns to scale, (b) strictly concave in its factors, (c) once continuously differentable, and (d) satisfies an Inada condition in each input. Let the price of the factors be given by wi > 0 for factors xi for i = 1, 2. Let the price of finished output good be p>0. a. Give an example of a production function that satisfies all the assumptions (a)-(d) above b. Give an example of a production function that satisfies all the assumptions (b)-(d) above except the technology is increasing returns to scale. c. State the firm's profit maximization problem for the case of Cobb Douglas production. d. Provide a picture with explanation of the profit maximizing factor inputs for a typical price p > 0 and factor price vector w > > 0. e. Obtain the first order conditions for this problem, and show that each factor will be used in a positive amount for each p > 0 and w > > 0. f. Using the envelope principle, what is the envelope of the profit function with respect to p, w1, and w2