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For Questions 1, consider the following classifications: Feasible Region I- Finite Line Segment II -Non-existent III...
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)...
Consider the following constraints and the c g graph below: Constraint L:4x-y21 Constraint 2: x+ys4 Constraint...
Consider the following constraints and the c g graph below: Constraint L:4x-y21 Constraint 2: x+ys4 Constraint 3:-x-4y 2-8 x, y20 4x-y=1 x-4y -8 a. (2 points) Shade the feasible region in the graph provided above. b. (1 point) For this part only the objective function is Minimize -2x + y. Which of the following describes the optimal solution? (Put a check next to your answer) Infeasible solution Unique optimal solution the point (4,0) minimizes the LP Alternate optimal solution Unbounded...
Consider the following product mix problem and its associated spreadsheet model. Max 3X1 + 3X2 Subject to:...
Consider the following product mix problem and its associated
spreadsheet model.
Max 3X1
+ 3X2
Subject to:
2X1
+ 3X2 ≤ 10 (constraint #1)
3X1
+ 2X2 ≤ 20 (constraint #2)
X1
≥
5 (constraint
#3)
X1,
X2 ≥
0 (non-negativity)
X1, X2>0 (non-negativity) A D E F B X1 С X2 1 Total Profit Number to make: Unit Profits: $3 $3 2 3 4 5 Slack/ Surplus Constraints L.H.S. 6 2 R.H.S. 10 20 5 7 2 3 2 0 3 8 3 1...
QUESTION 1 Given the following LP, answer questions 1-10 Minimize -3x15x2 Subject to: 3x2x 24 2x1+4x2 2 28 2s 6 x1, x2...
QUESTION 1 Given the following LP, answer questions 1-10 Minimize -3x15x2 Subject to: 3x2x 24 2x1+4x2 2 28 2s 6 x1, x2 20 How many extreme points exist in the feasible region for this problem? We cannot tell from the information that is provided The feasible e region is unbounded QUESTION 2 Given the following LP, answer questions 1-10 Minimize 2- 31+5x2 Subject to: 3x2x 24 2x1+4x2228 t is the optimal solution? (2, 6) (0, 12) (5,4.5) None of the...
Please be clear graphic solution Question (4): Use the graphical solution to solve the following LP...
Please be clear graphic solution
Question (4): Use the graphical solution to solve the following LP problems through the following steps: a- Specify the feasible solution space b- Specify the basic feasible solutions Count the number of basic feasible solutions d- Draw the Isoprofit line direction e- Determine the optimal solution (Zmax Xop, X20p) Max Z=2x1 + x2 Subjected to: 5 x2 60 2x1 XI X2 10 3x1 x2 44 Xi, X2 > 0
Consider the following linear program Max 3xl +2x2 S.t 1x1 + 1x2 〈 10 3x1 1x2...
Consider the following linear program Max 3xl +2x2 S.t 1x1 + 1x2 〈 10 3x1 1x2 〈 24 1xl t 2x2< 16 And xl, x2> 0. a) Use Excel Solver to find the optimal solution to this problem. State the optimal values of xl, x2, and Z. b) Assume that the objective function coefficient for xl changes from 3 to 5. Does the optimal solution change? c) Assume that the objective function coefficient for x1 remains 3, but the objective...
questions 5 6 7 PARTILMULTIPLE CHOI how much or how many of something to produce, purchase, hire, etc. в, C. represent...
questions 5 6 7
PARTILMULTIPLE CHOI how much or how many of something to produce, purchase, hire, etc. в, C. represent the values of the constraints measure the objective function. D. must exist for each constraint. PNDVS 2. Which of the following statements is NOT true? A. A feasible solution satisfies all constraints. B. An optimal solution satisfies all constraints. C An infeasible solution violates all constraints. D. A feasible solution point does not have to lie on the boundary...
[4.37] Consider the following problem: Maximize 2x + 3x2 subject to X1 + 2x2 5 10...
[4.37] Consider the following problem: Maximize 2x + 3x2 subject to X1 + 2x2 5 10 -*1 + 2x2 s 6 *1 + *2 S6 12 0. a. c. X1, Solve the problem graphically and verify that the optimal point is a degenerate basic feasible solution. b. Solve the problem by the simplex method. From Part (a), identify the constraint that causes degeneracy and resolve the problem after deleting this constraint. Note that degeneracy disappears and the same optimal solution...
Consider the following linear program: Maximize-2ri+ 2 subject to: 12x1 + 3x2 6, #7 10, i...
Consider the following linear program: Maximize-2ri+ 2 subject to: 12x1 + 3x2 6, #7 10, i 20 x2 20. a) Draw a graph of the constraints and shade in the feasible region. Label the vertices of this region with their coordinates. b) Using the graph obtained in (a). find the optimal solution and the maximum value of the objective function. c) What is the slack in each of the constraints?
Use the following Management Scientist output to answer the questions. LINEAR PROGRAMMING PROBLEM MAX 31X1+35X2+32X3 S.T....
Use the following Management Scientist output to answer the questions. LINEAR PROGRAMMING PROBLEM MAX 31X1+35X2+32X3 S.T. 3X1+5X2+2X3>90 6X1+7X2+8X3<150 5X1+3X2+3X3<120 OPTIMAL SOLUTION Objective Function Value = 763.333 Variable Value Reduced Cost X1 13.333 0.000 X2 10.000 0.000 X3 0.000 10.889 Constraint Slack/Surplus Dual Price 1 0.000 0.778 2 0.000 5.556 3 23.333 0.000 OBJECTIVE COEFFICIENT RANGES Variable Lower Limit Current Value Upper Limit X1 30.000 31.000 No Upper Limit X2 No Lower Limit 35.000 36.167 X3 No Lower Limit 32.000 42.889...
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)...
Consider the following constraints and the c g graph below: Constraint L:4x-y21 Constraint 2: x+ys4 Constraint 3:-x-4y 2-8 x, y20 4x-y=1 x-4y -8 a. (2 points) Shade the feasible region in the graph provided above. b. (1 point) For this part only the objective function is Minimize -2x + y. Which of the following describes the optimal solution? (Put a check next to your answer) Infeasible solution Unique optimal solution the point (4,0) minimizes the LP Alternate optimal solution Unbounded...
Consider the following product mix problem and its associated
spreadsheet model.
Max 3X1
+ 3X2
Subject to:
2X1
+ 3X2 ≤ 10 (constraint #1)
3X1
+ 2X2 ≤ 20 (constraint #2)
X1
≥
5 (constraint
#3)
X1,
X2 ≥
0 (non-negativity)
X1, X2>0 (non-negativity) A D E F B X1 С X2 1 Total Profit Number to make: Unit Profits: $3 $3 2 3 4 5 Slack/ Surplus Constraints L.H.S. 6 2 R.H.S. 10 20 5 7 2 3 2 0 3 8 3 1...
QUESTION 1 Given the following LP, answer questions 1-10 Minimize -3x15x2 Subject to: 3x2x 24 2x1+4x2 2 28 2s 6 x1, x2 20 How many extreme points exist in the feasible region for this problem? We cannot tell from the information that is provided The feasible e region is unbounded QUESTION 2 Given the following LP, answer questions 1-10 Minimize 2- 31+5x2 Subject to: 3x2x 24 2x1+4x2228 t is the optimal solution? (2, 6) (0, 12) (5,4.5) None of the...
Please be clear graphic solution
Question (4): Use the graphical solution to solve the following LP problems through the following steps: a- Specify the feasible solution space b- Specify the basic feasible solutions Count the number of basic feasible solutions d- Draw the Isoprofit line direction e- Determine the optimal solution (Zmax Xop, X20p) Max Z=2x1 + x2 Subjected to: 5 x2 60 2x1 XI X2 10 3x1 x2 44 Xi, X2 > 0
Consider the following linear program Max 3xl +2x2 S.t 1x1 + 1x2 〈 10 3x1 1x2 〈 24 1xl t 2x2< 16 And xl, x2> 0. a) Use Excel Solver to find the optimal solution to this problem. State the optimal values of xl, x2, and Z. b) Assume that the objective function coefficient for xl changes from 3 to 5. Does the optimal solution change? c) Assume that the objective function coefficient for x1 remains 3, but the objective...
questions 5 6 7
PARTILMULTIPLE CHOI how much or how many of something to produce, purchase, hire, etc. в, C. represent the values of the constraints measure the objective function. D. must exist for each constraint. PNDVS 2. Which of the following statements is NOT true? A. A feasible solution satisfies all constraints. B. An optimal solution satisfies all constraints. C An infeasible solution violates all constraints. D. A feasible solution point does not have to lie on the boundary...
[4.37] Consider the following problem: Maximize 2x + 3x2 subject to X1 + 2x2 5 10 -*1 + 2x2 s 6 *1 + *2 S6 12 0. a. c. X1, Solve the problem graphically and verify that the optimal point is a degenerate basic feasible solution. b. Solve the problem by the simplex method. From Part (a), identify the constraint that causes degeneracy and resolve the problem after deleting this constraint. Note that degeneracy disappears and the same optimal solution...
Consider the following linear program: Maximize-2ri+ 2 subject to: 12x1 + 3x2 6, #7 10, i 20 x2 20. a) Draw a graph of the constraints and shade in the feasible region. Label the vertices of this region with their coordinates. b) Using the graph obtained in (a). find the optimal solution and the maximum value of the objective function. c) What is the slack in each of the constraints?
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