Given the production function: y = f(x1, x2) = x1^1/2*x2^1/2 and p = 20, w1 = 4, W2 = 2 a. Find the demand functions that maximize profit, x1* (w1, w2, p) and x2* (w1, w2, p). b. Find the supply function: y* (w1, w2, p) = f(x1* (w1, w2, p), x2* (w1, w2, p)). C. Find the profit function, substituting the optimal demands in the profit equation TI(w1, w2, p) = p. y(x1* (w1, w2, p), x2* (w1, w2, p)) - W1 x1* (w1, w2, p) - W2. a. For the given prices, find the demanded quantities of the factors and the supplied quantity; b. Get the long-term maximum profit demands and the long-term product supply from the profit function, by Hotelling's lemma. C. Assuming x2bar = x2* that is, the value of x2* found in "d", obtain the short-run demand function for the factor x1 that maximizes short-run profit; Find the quantity demanded of the factor xl and compare with the quantity found in the letter d. d. If w1 = 5, what amount of x1 will maximize short-run profit? e. Find the Short Term Offer function. What is the quantity offered in the short term for w1 = 4 and w1 = 5