isi 2012 sample paper

[manvi ahuja]

Q12...suppose  (x*,y*) solves:
minimise   ax+by
subject to x^@ + y^@=M
where x,y>=O,a>b>O,M>O & @>1..then the solution is....
a.x*^@-1/y*^@-1=a/b
b.x*=O,y*=M^1/@
c. y*=0,x*=M^1/@
d.none of the above

[manvi ahuja]

Q.20.if a^2+b^2+c^2=1 then ab+bc+ca is...
a. -0.75
b.belongs to interval [-1,-0.5]
c..belongs to interval [0.5,1]
d.none of the above.

[duck]

Hi Manvi.. :)

Q1) x=0 and y=M^1/@

Q2) none of the above.

[manvi ahuja]

hi duck...
can u pls tell me the steps that hw u arrived at the answer...???

[duck]

Hi manvi.. :)

Q1) As the constraint is concave (@>1) therefore, you'll have corner solutions.
Now, they asked you to minimise the objective function and it will be minimised when x=0 and y=M^@
You can assume some values of a, b and @ to get some idea of this problem.


Q2) Take a=b=0 and c=1
=> a^2+b^2+c^2=1
and ab+ac+ba= 0
So, you can rule out options (a), (b) and (c).
Therefore, option(d) is the answer.