hi pls look at the attachment for the question to be answered

Question 4. [10 points] Consider a rm with cost function 1 l 2 c(w,r,q)=w2r2q where (w, r) are prices of labor and capital inputs, q is the quantity of output. Assume w > 0 and r > 0 and p is the market price of the rm's output. Answer the following questions. 1. Write out the rm's prot maximizing problem. Derive the rst order conditions for the rm's prot maximizing problem. Derive the rm's supply equation for output. (7) 2. Use Hotelling's Lemma to derive the rm's prot maximizing input demand equations for capital and labor, i.e. 1*(p, w, r) and k* (p, w, r). (3)