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
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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
For the given LP formulation, find the optimal solution using excel solver. Max(Z) = 5X1 + 8X2 Constraints : 2X1 + 4X2 <= 40 6X1 + 3X2 <= 42 X1 >= 3 X1,X2 >= 0 (a) Insert below a screenshot of the excel solver with final answers in it. (b) Write clearly which constraints are binding and which are non binding. (c) How much change can we make in the first constraint without changing the optimal solution for Z. (d)...
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
Consider the following LP max z=3x1+x2 s.t. −2x1 + x2 ≤ 3 x1 + 2x2 ≤ 5 x1,x2 ≥0 (a) Find the dual (or shadow) prices of the binding constraints (b) Find the dual (or shadow) prices of the binding “dual” constraints.