Optimization: transformation of target function and conditions
In a recent microeconomics lecture I was confronted with the following problem:
maxx1, x2, x3 2*sqrt(x1)
the professor reformulated the problem without explanation to
maxx1, x2, x3 4x1
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
Re: Optimization: transformation of target function and conditions
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.