1. Let y : f($1, m2) : f(m) be a production function that is asssumed to be either decreasing or constant returns to scale, the price of y is p, and the factor prices are given by w: wage (with :31 intrepreted as labor), and r: rental price of capital (where $2 is interpreted as capital). a. Write down the longrun prot maxmization problem. b. Is it possible that this problem does not have a solution for all (p,w,r)? c. Now, write down the Short run prot maximization problem assuming factor 1 is xed in the shortrun. What is "xed cost " here? What is variable cost? What is the rst order condition for this problem (assume the technology is smooth, and d. Compute the envelope theorem for the shortrun prot in the xed factor (factor 1). e. Now, maximize the Short run prot choosing the xed factor, and give the FCC. f. Explain the relationship between your answer in (a) and this answer in (d) g. Draw a detailed picture of the longrun prot maximization problem explaining everything in the picture completely