Solve the following linear programming model graphically: Max Z= 3x1 +4x2 Subject to: 2x1 + 4x2...

Solve the following linear programming model graphically:

Max Z= 3x1 +4x2

Subject to: 2x1 + 4x2 <= 22

-x1 + 4x2 <= 10

4x1 – 2x2 <= 14 x1 – 3x2 <= 1

x1, x2, >=0

Clearly identify the feasible region, YOUR iso-profit line and the optimal solution (that is, d.v. values and O.F. Value.

Expert Solution

Colby Messinger answered 1 year ago

Consider the following linear programming problem: Max Z = 3x1 + 3x2 Subject to: ...

Consider the following linear programming problem: Max Z = 3x1 + 3x2 Subject to: 10x1 + 4x2 ≤ 60 25x1 + 50x2 ≤ 200 x1, x2 ≥ 0 Find the optimal profit and the values of x1 and x2 at the optimal solution.

Exercise Solve the following linear programs graphically. Maximize Z = X1 + 2X2 Subject to 2X1...

Exercise Solve the following linear programs graphically. Maximize Z = X1 + 2X2 Subject to 2X1 + X2 ≥ 12 X1 + X2 ≥ 5 -X1 + 3X2 ≤ 3 6X1 – X2 ≥ 12 X1, X2 ≥ 0

Consider the following linear programming problem Maximize 6x1 + 4x2 + 5x3 Subject to: 2x1 +...

Consider the following linear programming problem Maximize 6x1 + 4x2 + 5x3 Subject to: 2x1 + 3x2 + x3 ≥ 30 2x1 + x2 + x3 ≤ 50 4x1 + 2x2 + 3x3 ≤ 120 x1, x2, x3 ≥ 0 a) Find the optimal solution by using simplex method b) Find the dual price for the first constraint. c) Find the dual price for the second constraint. d) Find the dual price for the third constraint. e) Suppose the right-hand...

Consider the following Integer Linear Programming (ILP) model Maximize Z = X1 + 4X2 Subject to...

Consider the following Integer Linear Programming (ILP) model Maximize Z = X1 + 4X2 Subject to X1 + X2 < 7 // Resource 1 –X1 + 3X2 < 3 // Resource 2 X1, X2 > 0 X1, X2 are integer i. Consider using the Branch and Bound (B & B) technique to solve the ILP model. With the help of Tora software, draw the B & B tree. Always give priority for X1 in branching over X2. Clearly label the...

Consider the following linear optimization model. Z = 3x1+ 6x2+ 2x3 st 3x1 +4x2 + x3...

Consider the following linear optimization model. Z = 3x1+ 6x2+ 2x3 st 3x1 +4x2 + x3 ≤2 x1+ 3x2+ 2x3 ≤ 1 X1, x2, x3 ≥0 (10) Write the optimization problem in standard form with the consideration of slack variables. (30) Solve the problem using simplex tableau method. (10) State the optimal solution for all variables.

Solve the following linear programming problem using generalised simplex method Maximise z= 2x1+3x2 subject to -2x1+x2>=3...

Solve the following linear programming problem using generalised simplex method Maximise z= 2x1+3x2 subject to -2x1+x2>=3 3x1+x2<=5 x1,x2>=0

Given the following LP max z = 2x1 + x2 + x3 s. t. 3x1 -...

Given the following LP max z = 2x1 + x2 + x3 s. t. 3x1 - x2 <= 8 x2 +x3 <= 4 x1,x3 >= 0, x2 urs (unrestricted in sign) A. Reformulate this LP such that 1)All decision variables are non-negative. 2) All functional constraints are equality constraints B. Set up the initial simplex tableau. C. Determine which variable should enter the basis and which variable should leave.

For the following linear programming problem: Maximize z = 2x1+ x2 Such that ...

For the following linear programming problem: Maximize z = 2x1+ x2 Such that x1+ 2x2 ≤ 12 x2 ≥ 3 x1,x2 ≥ 0 (a) Write the first two constraints in equation form by adding slack or subtracting excess (surplus) variables. (b)Find all basic solutions for this LP (c) Which of these solutions are feasible? (d)Which of these feasible solutions is optimal? Find the optimal value of z

Max Z = 2x1 + 8x2 + 4x3 subject to 2x1 + 3x2 ≤ 8 2x2...

Max Z = 2x1 + 8x2 + 4x3 subject to 2x1 + 3x2 ≤ 8 2x2 + 5x3 ≤ 12 3x1 + x2 + 4x3 ≤15 and x1,x2,x3≥0; Indicate clearly the optimal basic and nonbasic variables and their values and write the reduced cost of each optimal nonbasic variable.

MAX Z = 2x1 + 8x2 + 4x3 subject to 2x1 + 3x2 <= 8 2x2...

MAX Z = 2x1 + 8x2 + 4x3 subject to 2x1 + 3x2 <= 8 2x2 + 5x3 <= 12 3x1 + x2 + 4x3 <= 15 x1 + x3 = 11 and x1,x2,x3 >= 0 apply the Dual Simplex Method to recover feasibility.

Question