' D'''.; ' ' "' ___ ' _J__'__? .x __- problem: .___ ._ _ ___ . \"'0 ____ _____ "\"'O r ______________ min firs, y) = my 43: st 9101:, y) = 1:2 + 3y2 S 18 920139) = y S 1 (a) Write the Lagrange function for the minimization problem. Now change the minimum function to a maximum function (i.e. mazr f(:r, y) = my 43:) and provide the Lagrange function for the maximiza- :3} tion problem with the same constraints 91 and 92. [2pts] NOTE: The maximization problem is only for part (a). (b) List the names of all 4 groups of KKT conditions and their corresponding mathematical equations or inequalities for this specic minimization problem. [2pts] (c) Solve for 4 possibilities formed by each constraint being active or inactive. Do not forget to check the inactive constraints for each point when applicable. Candidate points must satisfy all the conditions mentioned in part b). [7pts] ((1) List the candidate point(s) (there is at least 1) obtained from part c). Please round answers to 3 decimal points and use that answer for calculations in further parts. This part can be completed in one line per candidate point. [2pts] (e) Find the one candidate point for which f (11:, y) is smallest. Check if 11(5):, y) is concave or convex at this point by using the llcssian in the second partial (.lcrivativc test. [2pts]