The simplex algorithm has been used to resolve the following problems, and the corresponding initial and nal tableaux are given (with the w row omitted). For each, a construct the dual (but do not solve it using simpex method} 0 determine the optimal valne(s) of the objective function for the primal and the dual. 0 determine an optimal solution point to the primal using the data from the tableaux. 0 determine an optimal solution point to the M using the data from the tableaux. Minimize 2.x] + 512 +913 subject to 2x: + 5x; 2 1 3x1 1'3 # x3 5 6 23:1 ~4xg+ x3=3 1|,.t2..t3 3: U Maximise ixl l2x2 + 1113 subject to 6x. 7x2+8x3=90 x1 + 3x3 2 42 athlete's 2 0