I'm trying to do the problem below and I cannot understand what (ii), (iv) and (v) are asking for.
From my understanding, Chebyshev approximation is used to transform a norm approximation problem in $l_{\infty}$ to a linear programming problem. So how should I apply Chebyshev approximation to $l_{1}$ and $l_{2}$ norm? Moreover, how should I "reformulate" the Chebyshev approximation problem using $l_{1}$ and $l_{\infty}$ as a LP?