AMIt SIR..help needed ..PLS HELP!!!!Dse 2007

[SoniaKapoor]

DSE 2007
q27-3

[Amit Goyal]

This is a standard optimization problem. You may use the graphical method and plot the constraints, make the indifference curves and figure out the optimal solution.

[kangkan]

@ sonia

Hi...we know that the the pic that optimum will be where the indiff curve is tangent to the budget curve..

Slope of indiff curve =2y/x ....slope of budget curve is 2x/2y

Equatiing we get, x= root over 2*y

now this must satisfy the equation of the circcle ..putiting it in X^2 +y^2=12, we get y=2 and X=rootover 8..ths satisfies the constraint that X<3 and Y<3..so no problem



I hope this helps

[SoniaKapoor]

Thanxx Amit Sir :)
Thanxx kangkan..pls help me with 30th also...

[kangkan]

Now,for 30..same technique...the circle must be the tangent to the Indiff curve which will be a straight line which will be a straight line with slope of -2....Applying the tangency condition we  have 2x/2y=2 or X=2y..but putting it in the eqn of the circle we get y=1.459 or X>3 which is not possible...therefore the optimum point(from the diagram will the boundary point ) x=3 and y=rootvor 3...hence option b :)