Consider the following lp (). min zeta = x_1 - 3x_2 - 5x_3 s. t. x_1 - 3x_2 greaterthanorequalto 3 (y_4) 7x_1 + 2x_2 + 5x_3 lessthanorequalto 20 (y_5) x_1 greaterthanorequalto 0; x_2 lessthanorequalto 0; x_3 greaterthanorequalto 0. reformulate lp () into a canonical form such that x_1 and x_2 are on the right-hand-side of the equations and x_3 is on the left-hand-side. there may exist multiple canonical forms that satisfy the above requirements and you only need to find one. the variables y_4 and y_5 are shadow prices of constraints (7) and (8). respectively. one possible solution is (x^*_1 = 0, x^*_2 = - l. x^*_3 = 4.4) and the shadow price is (y^*_4 = 1/3, y^*_5= -1). prove that the alleged solution (x^*_1 = 0. x^*_2 = - l, x^*_3 = 4.4) given in problem (1) is indeed optimal to lp (). do not assume without verification that the alleged shadow price (y^*_4 = 1/3, y^*_5 = -1) is the optimal dual solution.