1. Use the Big M method to find the optimal solution to the following LP:
Max z = 5x1 − x2
s.t.: 2x1 + x2 = 6
x1 + x2 ≤ 4
x1 + 2x2 ≤ 5
x1, x2 ≥ 0
Answer: z = 15, x1 = 3, x2 = 0.
1. Use the Big M method to find the optimal solution to the following LP: Max...
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.
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
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
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...
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
use the Big M method to solve the following LPs: 2 max z = x1 + x2 s.t. 2x1 + x2 > 3 3x1 + x2 < 3.5 X1 + x2 < 1 X1, X2 > 0
Please use the big M method to solve the following linear program. Write down all tableau, note basic variables and nonbasic variables. Use slack and artificial variables. Construct your tableau iterations using the standard form of the program. For example first line z+2x1-2x2+2x3=0. If possible, STATE THE OPTIMAL SOLUTION AND THE OPTIMAL VALUE. Otherwise state why you cannot find them. Consider the following linear program: 2x3 max z= –2x1 + s.t. + -x1 21 > 0, 2x2 - 2x2 +...
Question 2: Identify which of Cases (1)--(4) apply to the following LP problem. max z = 2x1 – X2 s. t. X1 – X2 < 1 2x1 + x2 > 6 X1, X2 > 0 (1) unbounded LP (2) infeasible LP (3) unique optimal solution (4) multiple optimal solutions
(1) Convert the following LPs to standard form: 22 (a) max z 3x1 + 2x2 s.t. 21 < 40 X1 + x2 < 80 2x1 + x2 < 100 X1, X2 > 0 (b) max z = 2x1 s.t. X1 – X2 <1 2x1 + x2 > 6 X1, X2 > 0 (c) max z = 3x1 + x2 s.t. 1 > 3 X1 + x2 < 4 2x1 – X2 = 3 X1, X2 > 0
Problem A: Consider the following LP problem to answer Questions 4 and 5. Maximise z = 5x1 + 4x2 Subject to 6X1 + 4x2 < 24 X1 + 2x2 5 6 -X1 + x2 <1 X2 < 2 X1, X2 > 0 Question 4 Refer to Problem A: Which of the following statements is correct? (1) The optimal value of x1 is in the interval [10, 15). (2) The optimal valu X2 is in the rval [0, 5). (3) The...