Solve the linear programming problem by the simplex y2 - 2x +41 method. Minimize 11x + 4y subject to the constraints ys -x+48 shown on the right. y=-x+28 y²-x+6 x 20, y20 The minimum value of 11x + 4y is , which is attained for x = and y=. (Type integers or fractions.)

Question 2: (a) Give the definition of the double root of a function and sketch the graph of a function with two roots: a simple root, marked x, and a double root, marked x. (b) Find an unseen example of a function, f, with a double root, x. The function f should not be a polynomial but could be any rational or transcendental function. Perform enough iterations of Newton's algorithm, written as a fixed-point iteration Xn+1 = g(en), to infer the order and rate of convergence of the sequence of data produced. Prove this assertion by writing a Taylor series for g about x, in powers of (xn xx).