25. (5 marks) Consider the following function h: R2 + R, h(x,y) = xy?. + = We consider the problem of optimising this fu

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25 5 Marks Consider The Following Function H R2 R H X Y Xy We Consider The Problem Of Optimising This Fu 1 (190.65 KiB) Viewed 29 times

25. (5 marks) Consider the following function h: R2 + R, h(x,y) = xy?. + = We consider the problem of optimising this function subject to the condition that C(x, y) = x(1 - 0) – y2 = 0. x 1 — x = = i. (1 marks) Write down the Lagrange function L for this constrained optimisation problem. ii. (1 marks) Calculate the gradient VL. iii. (2 mark) By solving for the equation VL = (8) (), obtain four constrained stationary = 0 points. iv. (1 mark) Does the function h have a maximum value on the constrained curve C(x, y) = 0? If yes, determine this maximum value (with mathematical justifica- tion); if no, explain why h cannot attain a maximum.