Space is not working in latex

Question

I want to have the following output .

For this purpose , I have the following code .

\begin{align*}
                    Maximize     \mathbf{z = x_1+2x_2+3x_3}  
                                 \end{align*}
                             
                \begin{align*} 
                    Subject to  \mathbf{x_1 + \hspace{2cm}+2x_3 \leq 2  }\\
                                    \mathbf{ \hspace{2cm}x_2+2x_3 \leq 2 } \\   
                                    \mathbf{x_1  \geq 0 , x_2 \geq 0 , x_3 \geq 0}  
                             \end{align*}  

For this code , I have the following output :

I do not understand how to achieve my desired output . What have I to do ? Please help me .

Answer 1

I would rather suggest to reverse the first equation and align them or remove the text from the math alignment environment, making to alignments

\documentclass{article}
\usepackage{amsmath}


\boldmath

\begin{document}
\begin{align*}
 \text{Maximize\phantom{o}}   &&              x_1+2x_2+3x_3 &=  z    \\
 \text{Subject to} &&     x_1+ 2x_3 &  \leq 2 \\
                   &&      x_2+2x_3 &  \leq 2  \\   
                   && x_1  \geq 0 , x_2 \geq 0 , x_3 &\geq 0
\end{align*}  


Maximize
\begin{align*}
    &&              z &= x_1+2x_2+3x_3 
\end{align*}
subject to 
\begin{align*}
 &&     x_1+ 2x_3 &  \leq 2 \\
 &&      x_2+2x_3 &  \leq 2  \\   
 && x_1  \geq 0 , x_2 \geq 0 , x_3 &\geq 0
\end{align*}  

\end{document}

Answer 2

I would suggest you not use bold for the math terms: Rendering so much material in bold tends to make it look excessively heavy without enhancing the readability or intelligibility of what's being presented. I would use a common gather* environment for the four lines of display math, the shortintertext macro (provided by the mathtools package, which also loads the amsmath package), and a coupld of \phantom statements to help arrange the desired spacing on the first two lines follow "subject to".

\documentclass{article}
\usepackage{mathtools}
\setlength\textwidth{4in} % just for this example
\begin{document}
\noindent
Let us consider the following problem.
\begin{gather*}
\text{Maximize } z = x_1+2x_2+3x_3
\shortintertext{subject to}
x_1 \phantom{+x_2} +2x_3 \leq 2  \\
\phantom{x_1+}x_2+2x_3 \leq 2 \\
x_1  \geq 0 ,\quad x_2 \geq 0 , \quad x_3 \geq 0
\end{gather*}  
\end{document}

Personally, I prefer the look without the \phantom statements; see, e.g., Christian Hupfer's proposed solution.