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(Solved): QUESTION TWO (20 MARKS) a) Given Z=2x^(2)+y^(2)-12x-8y+50 i) Find the critical values. (4 marks) ii) ...



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)



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