. (75 points) Solve the following problems in the textbook: Problem 1 on page 171; Problem 6 on page 178; Problems 2 on page 189; Problem 1 on page 212; Problem 18 on page 214. PROBLEMS Group A 1 Even if an LP's initial tableau is nondegenerate, later tableaus may exhibit degeneracy. Degenerate tableaus often occur in the tableau following a tie in the ratio test. To illustrate this, solve the following LP: max z = 5x1 + 3x2 s.t. 4x + 2x2 = 12 4x1 + x2 = 10 x + x2 0 Use the Big M method to solve the followir 2 min z = 2x + 3x2 s.t. 2x1 + x2 2 4 x1 - x2 = -1 X1, X2 20 2 Use the simplex algorithm to solve the following LP: max z = 2x1 + x2 s.t. 3x1 + x2 = 6 x + x2 = 4 x1 = 0, x2 urs Group A 1 Use the simplex algorithm to find two optimal solutions to the following LP: max z = 5x1 + 3x2 + x3 s.t. x1 + x2 + 3x3 = 6 5x2 + 3x2 + 6x3 = 15 X3, X1, X2 2 0 212 CHAPTER 4 The Simplex Algorithm and Goa TABLE 75 X5 X6 rhs 1 0 C1 4 X2 C2 a X3 0 1 X4 0 0 os T . (75 points) Solve the following problems in the textbook: Problem 1 on page 171; Problem 6 on page 178; Problems 2 on page 189; Problem 1 on page 212; Problem 18 on page 214. PROBLEMS Group A 1 Even if an LP's initial tableau is nondegenerate, later tableaus may exhibit degeneracy. Degenerate tableaus often occur in the tableau following a tie in the ratio test. To illustrate this, solve the following LP: max z = 5x1 + 3x2 s.t. 4x + 2x2 = 12 4x1 + x2 = 10 x + x2 0 Use the Big M method to solve the followir 2 min z = 2x + 3x2 s.t. 2x1 + x2 2 4 x1 - x2 = -1 X1, X2 20 2 Use the simplex algorithm to solve the following LP: max z = 2x1 + x2 s.t. 3x1 + x2 = 6 x + x2 = 4 x1 = 0, x2 urs Group A 1 Use the simplex algorithm to find two optimal solutions to the following LP: max z = 5x1 + 3x2 + x3 s.t. x1 + x2 + 3x3 = 6 5x2 + 3x2 + 6x3 = 15 X3, X1, X2 2 0 212 CHAPTER 4 The Simplex Algorithm and Goa TABLE 75 X5 X6 rhs 1 0 C1 4 X2 C2 a X3 0 1 X4 0 0 os T