please find the solution of this attached file

1. Firm is producing three goods chair (C), table (t) and sofa (S) with processed woods. De- mand Function for chair C=200-6Pc+2Pt-2Ps, demand function for table T=360+2PC-8Pt+4PS and demand function for sofa S=400+4Pc+2Pt-10Ps where total cost TC=2C2+472+252+2CT+2TS+2CS optimize the profit function using Hessian. Where C, T, and S represents quantity of chair, table and sofa and Pc, Pt, Ps represents the respective price of them. 2. A consumer utility function is given below U= X1X2 and her budget constraint B is a combination X1 x21+r, where r is the interest rate and r-20. Now find the optimum value using necessary conditions for constrained optimization and also show the sufficient conditions using Bordered Hessian. Give your justification why it is an optimum point