If is at a maximum, then so is . The changes made to the conditions are similar - taking the 4th power of both sides and squaring both sides.
- Hollywood
In a recent microeconomics lecture I was confronted with the following problem:
max_{x1, x2, x3} 2*sqrt(x_{1})
s.t.
2*sqrt(x_{2}y)=64
y=2*sqrt(2x_{3})
x_{1}+x_{2}+x_{3}=112
the professor reformulated the problem without explanation to
max_{x1, x2, x3} 4x_{1}
s.t.
16x_{2}^{2}y_{2}^{2}=64^{4 }y^{2}=8x_{3}
x_{1}+x_{2}+x_{3}=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