(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
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
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
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 +...
samplex
Problem1: Solve the following problem using simplex method: Max. z = 2 x1 + x2 – 3x3 + 5x4 S.t. X; + 7x2 + 3x3 + 7x, 46 (1) 3x1 - x2 + x3 + 2x, 38 .(2) 2xy + 3x2 - x3 + x4 S 10 (3) E. Non-neg. x > 0, x2 > 0, X3 > 0,44 20 Problem2: Solve the following problem using big M method: Max. Z = 2x1 + x2 + 3x3 s.t. *+...
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
Problem 01: Solve the LP problem using the graphic method Max Z = 30x1 + 50x2 St. 10x1 + 15x2 < 150 3x1 + 5x2 < 40 X1 2 3 X2 2 2 X1, X2 0
Solve this problem using the two-phase method. What special case do you observe? Max Zz4X1-2X2+X3 X1+2X2+X3 3 2X1-3X2+6X3 100 X1,X2,X3>0
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.
Use the simplex method to solve the following maximum problem: Maximize P= x1 +2:02 Subject to the constraints: 2x1 + x2 < 8 21 +2y < 5 X1 > 0 22 > 0 and using your final tableau answer the questions below by entering the correct answer in each blank box. Please enter fractions as 3/5, -4/7, and so on. 21 2 P=