Please write details of the process including calculations, graphs, and text and question numbers and answer all questions please, thank you

3. [30 MARKS] Let t be the 7\" digit of your Student ID. Consider the utility function 1 l \"(55, y) = mm\" + 37) 'l' mlnll + y) (a) [10 MARKS] Compute the Hessian matrix D2u(m,y). Is 11. concave or convex? (b) [4 MARKS] Give the formal definition of a convex set. (c) [8 MARKS] Using your conclusion to (a), show that I"+(1) = {(x,y) E R2 : u(x,y) 2 1} is a convex set. (d) [8 MARKS] Compute the 2nd order Taylor polynomial of u(9:,y) at (0,0)