Given: Objective function: maximize Z = 6x1+ 7x2 Constraints: x1 + 3 x2 30 4...
Given: Objective function: maximize Z = 6x1+ 7x2 Constraints: x1 + 3 x2 30 4 x1 + x2 32 x1 ≥ 0, x2 ≥ 0 a) Use graphical method to determine the optimal solution and the optimal value for Z.Use EXCEL to determine the optimal solution and the optimal value for Z.
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Given: Objective function: maximize Z = 6x1+ 7x2 Constraints: x1
+ 3 x2 30 4...
(1 point) Use the graphical method to maximize P = 6x1 + 4x2 subject to x1...
(1 point) Use the graphical method to maximize P = 6x1 + 4x2 subject to x1 2x1 x1 + + + x2 3x2 2x2 > 11 30 5 22 x120 x2 > 0 If there are no solutions, enter DNE in each box. Maximum value is P = where x1 = and x2 =
Question 12 Convert the constraints into linear equations by using slack variables. Maximize z = X1...
Question 12 Convert the constraints into linear equations by using slack variables. Maximize z = X1 + 2x2 + 3x3 Subject to: X1 + 9x2 + 3x3 = 40 6X1 + X2 + 6x3 s 50 X120,X220, X320 O X1 + 9x2 + 3x3 = 51 +40 6x1 + x2 +6x3 = S2 + 50 O X1 +9x2 + 3x3 +51 = 40 6x1 + x2 + 6x3 +S2 = 50 X1 +9x2 + 3x3 +51 = 40 6X1 +...
Maximize Z 34 X1 43 X2 29 X3 Subject to: 5 X1 + 4 X2+ 7...
Maximize Z 34 X1 43 X2 29 X3 Subject to: 5 X1 + 4 X2+ 7 X3 s50 1X1+2X2+2X3s16 3 X14 X2+1 X3 s 9 all Xi are integer and non-negative Use Excel QM. If one uses the optimal solution presented, how much slack is there in the first constraint equation? 03
Q4. (Sensitivity Analysis: Adding a new constraint) (3 marks) Consider the following LP max z= 6x1+x2 s.t.xi + x2 S5 2x1 + x2 s6 with the following final optimal Simplex tableau basis x1 r2 S2 rhs 0...
Q4. (Sensitivity Analysis: Adding a new constraint) (3 marks) Consider the following LP max z= 6x1+x2 s.t.xi + x2 S5 2x1 + x2 s6 with the following final optimal Simplex tableau basis x1 r2 S2 rhs 0 0 18 0.5 0.5 0.5 0.5 x1 where sı and s2 are the slack variables in the first and second constraints, respectively (a) Please find the optimal solution if we add the new constraint 3x1 + x2 S 10 into the LP (b)...
3. Problem 4-10 on p. 164: Find the optimal value of the objective function for the...
3. Problem 4-10 on p. 164: Find the optimal value of the objective function for the following problem by inspecting only its dual. (Do not solve the dual by the simplex method). Minimize z = 10x1 + 4x2 + 5x3 subject to 5x1 - 7x2 + 3x3 > 50 x1 > 0, x2 > 0, x3 0
For the given LP formulation, find the optimal solution using excel solver. Max(Z) = 5X1 +...
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)...
Vertex x1 x2 1 2 3 x1 x2 optimal vertex optimal objective function value
Vertex
x1
x2
1
2
3
x1
x2
optimal vertex
optimal objective function value
Consider the two-variable model where you want to maximize 2x1 + x2. There are three constraints:...
Consider the two-variable model where you want to maximize 2x1 + x2. There are three constraints: x1 + x2 <= 2, 4x1 + x2 <= 4, and -x1 + x2 <= 1. Also, x1and x2 are constrained to be nonnegative. Which of the following is the optimal solution? a. x1 = 2/3, x2 = 4/3 b. x1 = 0, x2 = 1 c. x1 = 1/2, x2 = 3/2 d. x1 = 2, x2 = 0
Using the Two-Phase method, Maximize z = 2x1-7x2 subject to 2xi + 3x2-3 4xi + 5x2...
Using the Two-Phase method, Maximize z = 2x1-7x2 subject to 2xi + 3x2-3 4xi + 5x2 2 10 6x1 + 7x2 3 4xi + 8x2 25
Figure 5 Constraint 2 Iso-profit line (objective function) 3 2 А B 4 x2 с 1...
Figure 5 Constraint 2 Iso-profit line (objective function) 3 2 А B 4 x2 с 1 6 Constraint 1 5 D E x1 24. For a problem with the same constraints as in figure 5 but a different objective function, it was found that the optimal solution was at point A. At point A, which constraint or constraints are binding? Select all that apply. a. X1 >=0 b. x2 >=0 C. Constraint 1 d. Constraint 2
(1 point) Use the graphical method to maximize P = 6x1 + 4x2 subject to x1 2x1 x1 + + + x2 3x2 2x2 > 11 30 5 22 x120 x2 > 0 If there are no solutions, enter DNE in each box. Maximum value is P = where x1 = and x2 =
Question 12 Convert the constraints into linear equations by using slack variables. Maximize z = X1 + 2x2 + 3x3 Subject to: X1 + 9x2 + 3x3 = 40 6X1 + X2 + 6x3 s 50 X120,X220, X320 O X1 + 9x2 + 3x3 = 51 +40 6x1 + x2 +6x3 = S2 + 50 O X1 +9x2 + 3x3 +51 = 40 6x1 + x2 + 6x3 +S2 = 50 X1 +9x2 + 3x3 +51 = 40 6X1 +...
Maximize Z 34 X1 43 X2 29 X3 Subject to: 5 X1 + 4 X2+ 7 X3 s50 1X1+2X2+2X3s16 3 X14 X2+1 X3 s 9 all Xi are integer and non-negative Use Excel QM. If one uses the optimal solution presented, how much slack is there in the first constraint equation? 03
Q4. (Sensitivity Analysis: Adding a new constraint) (3 marks) Consider the following LP max z= 6x1+x2 s.t.xi + x2 S5 2x1 + x2 s6 with the following final optimal Simplex tableau basis x1 r2 S2 rhs 0 0 18 0.5 0.5 0.5 0.5 x1 where sı and s2 are the slack variables in the first and second constraints, respectively (a) Please find the optimal solution if we add the new constraint 3x1 + x2 S 10 into the LP (b)...
3. Problem 4-10 on p. 164: Find the optimal value of the objective function for the following problem by inspecting only its dual. (Do not solve the dual by the simplex method). Minimize z = 10x1 + 4x2 + 5x3 subject to 5x1 - 7x2 + 3x3 > 50 x1 > 0, x2 > 0, x3 0
Vertex
x1
x2
1
2
3
x1
x2
optimal vertex
optimal objective function value
Using the Two-Phase method, Maximize z = 2x1-7x2 subject to 2xi + 3x2-3 4xi + 5x2 2 10 6x1 + 7x2 3 4xi + 8x2 25
Figure 5 Constraint 2 Iso-profit line (objective function) 3 2 А B 4 x2 с 1 6 Constraint 1 5 D E x1 24. For a problem with the same constraints as in figure 5 but a different objective function, it was found that the optimal solution was at point A. At point A, which constraint or constraints are binding? Select all that apply. a. X1 >=0 b. x2 >=0 C. Constraint 1 d. Constraint 2
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