44. Consider the following linear program (LP) max z=4x114x2 Subject to 2x1 + 7x2 + x3 = 21 7x12x2+ x4 = 21 X1, X2, X3, X4 0. Each of the following cases provides an inverse matrix and its corresponding basic variables for the LP above. Determine whether or not each basic solution is feasible. Interpret these basic feasible solutions and hence find an optimal solution. Is the optimal solution unique? 0 7 (a) (X2, X4); (b) (X1, X4); - 12 727 - 7 0 1 2 45 17 45 (c) (X2, X1); 2 7 45 45 45. Consider an M/M/c queuing system with parameters and . Draw its state- transition rate diagram and find the steady-state probability distribution for number of customers in the system.