 # I have a very simple linear problem: <mtable columnalign="right left" rowspacing="3pt" column Brenden Tran 2022-06-23 Answered
I have a very simple linear problem:

Suppose I want to write this problem equivalently as in Find the equivalent linear program. Unlike the problem in the link, I have equality. Can I write it equivalently as:

The converse is intuitive: Given $\left\{x,\alpha ,\beta \right\}$ feasible for the second problem, adding the first and second constraints gives the constraint of the first problem. But the forward part is not clear, especially because I have never seen an equality constraint written like this. Any help would be highly appreciated.
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You are correct. Suppose $x$ is feasible. Then . Therefore any solution satisfying the latter conditions is also feasible.

A simple example to explain what I think is the part you are unclear about is the following. Look at the following two problems:
1.

2.

They obviously generate the same feasible solution; the constraint added is weaker than the existing constraint. Similarly the following problem also generates the same feasible solution: