Consider this system:

${e}_{i}={b}_{i}-\sum _{j=1}^{n}{a}_{i,j}{x}_{j}\phantom{\rule{0ex}{0ex}}(i=1,2,...m)$

where ${a}_{i,j}$ ($(1\le i\le m\phantom{\rule{thinmathspace}{0ex}},\text{}1\le \text{}j\le n)$) and $(1\le i\le m)$ are given. The problem is to find an assignment of values to the variables ${x}_{1},...,{x}_{n}$ that minimizes max $|{e}_{j}|$. Express this problem as a linear program in the standard form.

${e}_{i}={b}_{i}-\sum _{j=1}^{n}{a}_{i,j}{x}_{j}\phantom{\rule{0ex}{0ex}}(i=1,2,...m)$

where ${a}_{i,j}$ ($(1\le i\le m\phantom{\rule{thinmathspace}{0ex}},\text{}1\le \text{}j\le n)$) and $(1\le i\le m)$ are given. The problem is to find an assignment of values to the variables ${x}_{1},...,{x}_{n}$ that minimizes max $|{e}_{j}|$. Express this problem as a linear program in the standard form.