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1) Consider the simplex tableau obtained after a few iterations: RHS Basic 1 1/4 5/8 57/4 57/4 0 ...
4) (20 pts) Consider the following optimal Simplex Tableau of an LP problem: 11 12 13...
4) (20 pts) Consider the following optimal Simplex Tableau of an LP problem: 11 12 13 0 0 0 14 -4 1 RHS -2-40 0 1 1 1 It is known that 14 and 15 are the slack variables in the first and the second constraints of the original problem. The constraints are stype. Write the original problem.
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)...
2. Consider the linear programm (a) Fill in the initial tableau below in order to start...
2. Consider the linear programm (a) Fill in the initial tableau below in order to start the Big-M Method tableau by performing one pivot operation. (6) The first tableau below is the tableau just before the optimal tableau, and the second one oorresponds to the optimal tableau. Fill in the missing entries for the second one. 1 7 56 M15 25 01 3/2 2 0 0 1/2 0 15/2 #310 0 5/2-1 o 1-1/2 0133/2 a1 a rhs (i) Exhibit...
SOLVE STEP BY STEP! 4. Consider the following LP: Minimize z = x; +3x2 - X3...
SOLVE STEP BY STEP!
4. Consider the following LP: Minimize z = x; +3x2 - X3 Subject to x + x2 + x2 > 3 -x + 2xz > 2 -x + 3x2 + x3 34 X1 X2,43 20 (a) Using the two-phase method, find the optimal solution to the primal problem above. (b) Write directly the dual of the primal problem, without using the method of transformation. (c) Determine the optimal values of the dual variables from the optimal...
This is question 5.3-5 from Introduction to Operations Research (Hillier). Relevant text: Consider the following problem....
This is question 5.3-5 from Introduction to Operations Research
(Hillier). Relevant text:
Consider the following problem. Maximize Z= cixi + c2x2 + C3X3 subject to x1 + 2x2 + x3 = b 2x1 + x2 + 3x3 = 2b and x 20, X220, X2 > 0. Note that values have not been assigned to the coefficients in the objective function (C1, C2, C3). and that the only specification for the right-hand side of the functional constraints is that the second...
eclass.srv.ualberta.ca 2 of 2 1. Consider the matrix 3-2 1 4-1 2 3 5 7 8...
eclass.srv.ualberta.ca 2 of 2 1. Consider the matrix 3-2 1 4-1 2 3 5 7 8 (a) Find a basis B for the null space of A. Hint: you need to verify that the vectors you propose 20 actually form a basis for the null space. (Recall: (1) the null space of A consists of all x e R with Ax = 0, and (2) the matrix equation Ax = 0 is equivalent to a certain system of linear equations.)...
3 Gepbab Production Company uses labor and raw material to produce three products. The resource requirements...
3 Gepbab Production Company uses labor and raw material to produce three products. The resource requirements and sales price for the three products are as shown in Table 10. Currently, 60 units of raw material are available. Up to 90 hours of labor can be purchased at Sl per hour. To maximize Gepbab profits, solve the following LP: max z = 6X1 + 8X2 + 13X3 - L s.t. 3X1 + 4X2 + 6X3 - LS 0 2X1 + 2X2...
Exercise 2 Linear Programming 1. The Scrod Manufacturing Co. produces two key items – special-purpose Widgets...
Exercise 2 Linear Programming 1. The Scrod Manufacturing Co. produces two key items – special-purpose Widgets (W) and more generally useful Frami (F). Management wishes to determine that mix of W & F which will maximize total Profits (P). Data W F Unit profit contributions $ 30 $ 20 Demand estimates (unit/week) 250 500 Average processing rates – each product requires processing on both machines (units/hour) Machine #1 2 4 Machine #2 ...
1/ Consider the following table. Defects in batch Probability 2 0.18 3 0.29 4 0.18 5...
1/ Consider the following table. Defects in batch Probability 2 0.18 3 0.29 4 0.18 5 0.14 6 0.11 7 0.10 Find the standard deviation of this variable. 1.52 4.01 1.58 2.49 2/ The standard deviation of samples from supplier A is 0.0841, while the standard deviation of samples from supplier B is 0.0926. Which supplier would you be likely to choose based on these data and why? Supplier B, as their standard deviation is higher and, thus, easier to...
1. COMPUTER PRODUCTION. MVC Enterprises can manufacture four different computer models; the Student, Plus, Net, and...
1. COMPUTER PRODUCTION. MVC Enterprises can manufacture four different computer models; the Student, Plus, Net, and Pro models. The following gives the configurations of each model Student Celeron 20 gb Plus Pentium 20 gb Net Celeron 20 gb Pro Pentium 30 gb NO YES CD R/W YES DVD DVD + CD R/W Processor Hard Drive Floppy Drives Zip Drive Audio/Video Monitor Case Production Times (hrs.) Unit Profit YES DVD + CD R/W 17" Tower 15" 15 17" Tower Mini-Tower Mini-Tower...
4) (20 pts) Consider the following optimal Simplex Tableau of an LP problem: 11 12 13 0 0 0 14 -4 1 RHS -2-40 0 1 1 1 It is known that 14 and 15 are the slack variables in the first and the second constraints of the original problem. The constraints are stype. Write the original problem.
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)...
2. Consider the linear programm (a) Fill in the initial tableau below in order to start the Big-M Method tableau by performing one pivot operation. (6) The first tableau below is the tableau just before the optimal tableau, and the second one oorresponds to the optimal tableau. Fill in the missing entries for the second one. 1 7 56 M15 25 01 3/2 2 0 0 1/2 0 15/2 #310 0 5/2-1 o 1-1/2 0133/2 a1 a rhs (i) Exhibit...
SOLVE STEP BY STEP!
4. Consider the following LP: Minimize z = x; +3x2 - X3 Subject to x + x2 + x2 > 3 -x + 2xz > 2 -x + 3x2 + x3 34 X1 X2,43 20 (a) Using the two-phase method, find the optimal solution to the primal problem above. (b) Write directly the dual of the primal problem, without using the method of transformation. (c) Determine the optimal values of the dual variables from the optimal...
This is question 5.3-5 from Introduction to Operations Research
(Hillier). Relevant text:
Consider the following problem. Maximize Z= cixi + c2x2 + C3X3 subject to x1 + 2x2 + x3 = b 2x1 + x2 + 3x3 = 2b and x 20, X220, X2 > 0. Note that values have not been assigned to the coefficients in the objective function (C1, C2, C3). and that the only specification for the right-hand side of the functional constraints is that the second...
eclass.srv.ualberta.ca 2 of 2 1. Consider the matrix 3-2 1 4-1 2 3 5 7 8 (a) Find a basis B for the null space of A. Hint: you need to verify that the vectors you propose 20 actually form a basis for the null space. (Recall: (1) the null space of A consists of all x e R with Ax = 0, and (2) the matrix equation Ax = 0 is equivalent to a certain system of linear equations.)...
3 Gepbab Production Company uses labor and raw material to produce three products. The resource requirements and sales price for the three products are as shown in Table 10. Currently, 60 units of raw material are available. Up to 90 hours of labor can be purchased at Sl per hour. To maximize Gepbab profits, solve the following LP: max z = 6X1 + 8X2 + 13X3 - L s.t. 3X1 + 4X2 + 6X3 - LS 0 2X1 + 2X2...
1. COMPUTER PRODUCTION. MVC Enterprises can manufacture four different computer models; the Student, Plus, Net, and Pro models. The following gives the configurations of each model Student Celeron 20 gb Plus Pentium 20 gb Net Celeron 20 gb Pro Pentium 30 gb NO YES CD R/W YES DVD DVD + CD R/W Processor Hard Drive Floppy Drives Zip Drive Audio/Video Monitor Case Production Times (hrs.) Unit Profit YES DVD + CD R/W 17" Tower 15" 15 17" Tower Mini-Tower Mini-Tower...
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