# Thread:

1. ## 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)
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

2. ## Re: Optimization: transformation of target function and conditions

If $2\sqrt{x_1}$ is at a maximum, then so is $4x_1=(2\sqrt{x_1})^2$. The changes made to the conditions are similar - taking the 4th power of both sides and squaring both sides.

- Hollywood
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.8817735314369202, "perplexity_flag": "middle"}