Solve the following LP problem by the dual simplex method

a) Exhibit the optimal primal solution and the corresponding optimal primal basis.

b) verify that the product of the optimal basis and its inverse is equal to an identity matrix.

c) Exhibit the dual optimal solution and verify that the dual ob ective function of the given problem, evaluated at the optimal dual variables, is equal to the optimal value of the primal ob ective function.

max Z = -1 -3x2 - 2x3 - (1/2)x4 -21-322-23 sub ect to 21+ 2x2+3x3 2x1+2+5x3 15 20 1+22+3+(1/2)x410 x; 0, j=1,....4.