(20 points) A price-taking rm, i.e., operating under perfect competition, seeks to maximize prots. The rm produces a good y, which sells it sells at price p, and faces costs of production given by 60:, ml, 1.02) = y2(w1 + 102), where ml and 102 are the prices of two inputs in the production of 3:. However, the rm faces uncertainty regarding the input price ml: with probability 6 the price is 1111,}, and with probability 1 9 the price is mm, with 101,}, > 101,1. (a) (10 points) State the rm's problem and solve for the supply function of the rm, i.e., the optimal value of y as a rnction of the prices and 6'. Be as rigorous as you can. (b) (10 points) Now suppose that ml is a continuous random variable that can take values on the interval [101,1, rum] and is distributed according to the probability density function 3. State the rm's problem and solve for the supply function. Be as rigorous as you can