1 | initial version |

Regarding 1, see the answer of https://ask.sagemath.org/question/47851/optimization-under-constraint

Regarding 2, which factorization would you expect ?

Regarding 3, you ar lucky because in the tree of the representation of the expression, `alpha+beta`

appears as subtrees, so the following works:

```
sage: U1.subs({alpha+beta:1})
A*(R*alpha/p_x)^alpha*(R*beta/p_y)^beta
```

Regarding 4, if you are using jupyter notebook, you can add the following in the first cell:

```
%display latex
```

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