In a recent microeconomics lecture I was confronted with the following problem:
maxx1, x2, x3 2*sqrt(x1)
s.t.
2*sqrt(x2y)=64
y=2*sqrt(2x3)
x1+x2+x3=112
the professor reformulated the problem without explanation to
maxx1, x2, x3 4x1
s.t.
16x22y22=644
y2=8x3
x1+x2+x3=112
and then solved by plugging the conditions into the target function. How can such a transformation be determined without changing the problem at hand? what is the logic or the reason behind this?
thanks for any clue