In order to implement complicated nonlinear functions in a computer, so- metimes polynomial approximations are used. in this exercise, we explore one way of computing these using linear programming. consider a scalar function f(x), which we are trying to approximate over the interval [a; b] with a polynomial p(x) of degree d. as a measure of how well the polynomial approximates the function, we can use the norm. || f – p||. : = sup if(x) – p(x)]. the minimax or chebyshev polynomial approximation of degree d of f(x) is then defined as min || f (x) – p(x) ||, where pa is the set of polynomials of degree less than or equal to d. because the true il . il norm can sometimes be troublesome to compute, throughout this exercise we will use instead a discrete approximation given by: ||g|| : = max g(xi)], where the ti is a set of n points equispaced on the interval. give a standard linear programming formulation of the chebyshev approximation problem in the || . ii norm.