QUESTION TWO (20 MARKS) a) Given
Z=2x^(2)+y^(2)-12x-8y+50
i) Find the critical values. (4 marks) ii) Prove that the critical values are at a relative maximum/ minimum. (4 marks) b) An individual's utility function is given by
U=260x_(1)+310x_(2)+5x_(1)x_(2)-10x_(1)^(2)-x_(2)^(2)
where
x_(1)
is the amount of leisure measured in hours per week and
x_(2)
is earned income measured in RM per week. i) Find the utility-maximising values of
x_(1)
and
x_(2)
. (6 marks) ii) Calculate the maximum utility. (2 marks) iii) Use the Hessian, prove that the utility is at a maximum. (4 marks)