Suppose the canonical form of a linear programming problem is given by the constraint matrix A and the rigth hand side vector b, where [3 0 1 1 0] A = 2 1 0 o 0 and b = |3 [4 0 3 0 1] [5] Determine (and justify) which of the following solution is (ii) (iii) (iv) a feasible solution to the linear programming problem an extreme point of the feasible region a basic solution a basic feasible solution For each basic feasible solution, list the basic variable. a. (0, 3, 0, 5, 6) b. (0, 3, 5, 0, -9) c. (3/2, 0, 0, 1/2, 0) d. (1/2, 1, 1, 0, 2) e. (1, 1, 1/2, 3/2, 1/2) 536

Linear Programming ass. b1 Minimize z = 0.6x1 + 0.35x2 subject to: 5x1 +7x2 2 8 4x1 + 2x2 2 15 2x1+ x2 2 3 x1 2 0, x2 2 0. Q2 Maximize Z = 250x +75y subject to the constraints: 5x + ys 100 X+ys 60 X2 0, y 20 Q3 maximize -x1+ 3x2 - 3x3 subject to 3x1- x2 - 2x3 <7 -2x1-4x2 + 4x3 <3 x1 - 2x3 <4 -2x1 + 2x2 + x3 < 8 3x1 <5 x1, x2, x3 2 0.

The initial tableau of a linear programming problem is given. Use the simplex method to solve the problem. X2 X3 4 4 2 3 X₁ 1 4 3 -1 $₁ 1 0 0 $2 0 1 0 Z 0 0 1 16 60 The maximum is when x₁ = x₂ = x3 = . $₁=₁ and $2 = | (Type integers or simplified fractions.)

Please don't provide handwritten solution

Use a graphing calculator or a computer program for the simplex method to solve this linear programming problem. S1 $2 X4 .625 1 0 .5 .375 0 1 0 0 0 0 X1 0 0 1 X2 X3 0 .375 .75 .25 125 0 -105-80 -75 - 65 S3 = 0 530 0 630 1 280 0 0 The optimal solution X₁ = ‚ X₂ = ₁ ×3 = (Do not round until the final answer. Then round to the nearest integer as needed.) and X4 = produces the maximum value