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.

Expert Solution

Please like ??

orchestra answered 1 year ago

Simplex Method Consider the following linear programming problem: max z = 6x1 + 3x2 - 9x2...

Simplex Method Consider the following linear programming problem: max z = 6x1 + 3x2 - 9x2 - 9x3 + 15x4 s.t. 2x1 + 4x2 +6x3 + 8x4 <= 80 6x1 - 3x2 +3x3 + 6x4 <= 24 12x1 - 6x2 + 3x3 - 3x4 <= 30 x1, x2, x3, x4 >= 0 Rewrite the problem in standard form, that is, add the necessary slack variables in order to consider only equality constraints (and non-negativity). What is the...

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.

Consider the following integer linear programming problem: Max Z = 4.2x + 4.8y + 5.6z Subject...

Consider the following integer linear programming problem: Max Z = 4.2x + 4.8y + 5.6z Subject to: 4x + 2y + 7z ≤ 37 4x + 4y + 5z ≤ 40 2.8y ≤ 10 x, y, z ≥ 0 and integer What is the optimal solution to the integer linear programming problem? State the optimal values of decision variables.

Consider the following linear program. Maximize z= 5x1+ 3x2 subject to 3x1+ 5x2≤15 5x1+ 2x2≤10 –...

Consider the following linear program. Maximize z= 5x1+ 3x2 subject to 3x1+ 5x2≤15 5x1+ 2x2≤10 – x1+ x2≤2 x2≤2.5 x1≥0, x2≥0 a. Show the equality form of the model. b. Sketch the graph of the feasible region and identify the extreme point solutions. From this representation find the optimal solution. c. Analytically determine all solutions that derive from the intersection of two constraints or nonnegativity restrictions. Identify whether or not these solutions are feasible, and indicate the corresponding objective function...

consider the linear programming problem maximize z = x1 +x2 subjected tp x1 + 3x2 >=...

consider the linear programming problem maximize z = x1 +x2 subjected tp x1 + 3x2 >= 15 2x1 + x2 >= 10 x1 + 2x2 <=40 3x1 + x2 <= 60 x1 >= 0, x2>= 0 solve using the revised simplex method and comment on any special charateristics of the optimal soultion. sketch the feasible region for the problem as stated above and show on the figure the solutions at the various iterations

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

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.

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.

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 programming problem: Maximize 16X + 14Y Subject to: 3X + 4Y ≤...

Consider the following linear programming problem: Maximize 16X + 14Y Subject to: 3X + 4Y ≤ 520 3X + 2Y ≤ 320 all variable ≥ 0 The maximum possible value for the objective function is

Question