3. Use the simplex algorithm to find an optimal solution to the following LP: s.t. 3x1...
Use the simplex algorithm to find all optimal solutions to the following LP. max z=2x1+x2 s.t. 4x1 + 2x2 ≤ 4 −2x1 + x2 ≤ 2 x1 ≥1 x1,x2 ≥0
2. Use the simplex algorithm to find an optimal solution to the following LP: max z 5x1 + 3x2 + x3 5x +3x2 +6x s 15
Use the two-phase method to find the optimal solution to the following LP: Min z = 3x1 + 2x2 s.t.: 3x1 + x2 ≥ 3 4x1 + 3x2 ≥ 6 x1 + 2x2 ≤ 3 x1, x2 ≥ 0 Answer: z = 4.2, x1 = 0.6, x2 = 1.2.
Use the Big M method to find the optimal solution to the following LP: min z = -3x1 + x2 s.t. X1 - 2x2 2 -x1 + x2 3 x1, x2 0 We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Consider the following LP problem: Minimize Cost = 3x1 + 2x2 s.t. 1x1 + 2x2 ≤ 12 2x1 + 3 x2 = 12 2 x1 + x2 ≥ 8 x1≥ 0, x2 ≥ 0 A) What is the optimal solution of this LP? Give an explanation. (4,0) (2,3) (0,8) (0,4) (0,6) (3,2) (12,0) B)Which of the following statements are correct for a linear programming which is feasible and not unbounded? 1)All of the above. 2)Only extreme points may be optimal....
please help! Use the Big M method to find the optimal solution to the following LP: max z = x1 + x2 s.t. 2x1 + x2 > 3 3x1 + x2 = 3.5 x1 + x2 = 1 X1, X2 = 0
Consider the following LP: Max x1 +x2 +x3 s.t. x1 +2x2 +2x3 ≤ 20 Solve this problem without using the simplex algorithm, but using the fact that an optimal solution to LP exists at one of the basic feasible solutions.
ALGORITHM DESIGN Write the following LP in standard form. max x_1 + 3x_2 + 2x_3 s.t. x_1 - x_2 + 2x_3 lessthanorequalto 5 2x_1 - x_2 lessthanorequalto 0 2x_2 + x_3 lessthanorequalto 5 x_1, x_2, x_3 greaterthanorequalto 0 (b) Write the Dual LP of the LP of part (a).[Use the usual dual format, that is, min{b^T y : A^T y greaterthanorequalto c, y greaterthanorequalto 0}.] (c) Run the simplex algorithm to obtain the optimal solution to the primal.
Question 3: Identify which of LP problems (1)--(4) has (x1,x2) = (20,60) as its optimal solution. (1) min z = 50xı + 100X2 s.t. 7x1 + 2x2 > 28 2x1 + 12x2 > 24 X1, X2 > 0 (2) max z = 3x1 + 2x2 s.t. 2x1 + x2 < 100 X1 + x2 < 80 X1 <40 X1, X2 > 0 (3) min z = 3x1 + 5x2 s.t. 3x1 + 2x2 > 36 3x1 + 5x2 > 45...
3. Use the two-phase simplex method to solve the following LP. Min z = x1 + 2x2 Subject to 3x1 + 4x2 < 12 2x1 - x2 2 2 X1, X2 20