![(a) (5 pts) Write the following LP in standard form. max 1 3r2 2r3 s.t. ri 213 S 5 2ri 2r2 (b) (5 pts) Write the Dual LP of the LP of part (a). see the usual d format, that is, mi y in AT y 2 c, 20).] (c) (5 pts) Run the simplex algorithm to obtain the optimal solution to the prima](http://img.homeworklib.com/questions/4706a380-b926-11eb-80b8-a19e91d16d36.png?x-oss-process=image/resize,w_560)
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ALGORITHM DESIGN
Write the following LP in standard form. max x_1 + 3x_2 + 2x_3 s.t....
Consider the following linear programming model Min 2X_1 + 3X_2 + X3 Subject to: X_1 +...
Consider the following linear programming model Min 2X_1 + 3X_2 + X3 Subject to: X_1 + X_2 + 5X_3 greaterthanorequalto 4 X_1 + X_3 greaterthanorequalto 2 -X_1 + X_2 + 3X_3 greaterthanorequalto 1 X_1, X_2, X_3 greaterthanorequalto 0 Consider the solution (X_1 = 1, X_2 = 3, X_3 = 1). At this solution, how many of the constraints are binding? A) 1 B) 2 C) 3 D) 4 E) 5
Use the simplex algorithm to find all optimal solutions to the following LP. max z=2x1+x2 s.t....
Use the simplex algorithm to find all optimal solutions to the following LP. max z=2x1+x2 s.t. 4x1 + 2x2 ≤ 4 −2x1 + x2 ≤ 2 x1 ≥1 x1,x2 ≥0
Consider the following LP: Max x1 +x2 +x3 s.t. x1 +2x2 +2x3 ≤ 20 Solve this...
Consider the following LP: Max x1 +x2 +x3 s.t. x1 +2x2 +2x3 ≤ 20 Solve this problem without using the simplex algorithm, but using the fact that an optimal solution to LP exists at one of the basic feasible solutions.
3. Use the simplex algorithm to find an optimal solution to the following LP: s.t. 3x1...
3. Use the simplex algorithm to find an optimal solution to the following LP: s.t. 3x1 +26 s.t.-xi + 2x2 S 0 レ
Question 1: Consider the following LP model. max ? = 4?1 + 4?2 s.t. 3?1 −...
Question 1: Consider the following LP model. max ? = 4?1 + 4?2 s.t. 3?1 − ?2 ≤ 9 ?1 + ?2 ≤ 7 5?2 ≤ 25 ?1 ≥ 0, ?2 ≥ 0 Part a) Find the optimal solution for the above model using simplex technique. Part b) Find the shadow prices (optimal dual variables) for the model. Part c) If you could buy an additional unit of the first resource for a cost of 5/2, would you do this?...
Without using the normal form, explicitly write the dual of the following primal problem. Min W...
Without using the normal form, explicitly write the dual of the following primal problem. Min W = 2y1 + 3y2 s.t. 0.5y1 + 0.25y2 <= 4 y1 + 3y2 >= 20 y1 + y2 = 10 y1, y2 >= 0 b) Using line 0 of the optimal table of the primal, which is below, obtain the solution of the dual problem, that is, obtain the values of the dual variables as well as the optimal value of the objective function...
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...
. Solve the following LP minimization problem. Min 3X + 2Y s.t. ...
. Solve the following LP minimization problem. Min 3X + 2Y s.t. 5X + 3Y <= 30 3X + 4Y >= 36 Y >= 7 X , Y >= 0 Group of answer choices X = 0, Y= 9 The optimal value of the objective function is 5. None of the other answers are correct. The optimal value of the objective function is 7. X = 1,...
Consider the following linear program: Max 2X + 3Y s.t. 5X +5Y ≤ 400 -1X+ 1Y...
Consider the following linear program: Max 2X + 3Y s.t. 5X +5Y ≤ 400 -1X+ 1Y ≥ 10 1X + 3Y ≥ 90 X, Y ≥ 0 a. Use the graphical solution procedure to find the optimal solution. b. Conduct a sensitivity analysis to determine the range of optimality for the objective function coefficients X & Y. c. What are the binding constraints? d. If the right-hand-side of the binding constraints are marginally increased, what will be the Dual Value?
Question 3 : Branch and Bound max 36a1282+8as s.t. 21i + 20r2 6xs 23 a e 10, 1]3 Write the LP Relaxation of this problem. 1. 2. What type of problem is this? (this type of problem has a particular na...
Question 3 : Branch and Bound max 36a1282+8as s.t. 21i + 20r2 6xs 23 a e 10, 1]3 Write the LP Relaxation of this problem. 1. 2. What type of problem is this? (this type of problem has a particular name) Solve this problem by branch-and-bound, using the branching rule for binary variables of branching o 3. the most fractional variable. On the next page, write down the branch-and-bound tree you obtained. a. Each node should include the solution letter,...
Consider the following linear programming model Min 2X_1 + 3X_2 + X3 Subject to: X_1 + X_2 + 5X_3 greaterthanorequalto 4 X_1 + X_3 greaterthanorequalto 2 -X_1 + X_2 + 3X_3 greaterthanorequalto 1 X_1, X_2, X_3 greaterthanorequalto 0 Consider the solution (X_1 = 1, X_2 = 3, X_3 = 1). At this solution, how many of the constraints are binding? A) 1 B) 2 C) 3 D) 4 E) 5
3. Use the simplex algorithm to find an optimal solution to the following LP: s.t. 3x1 +26 s.t.-xi + 2x2 S 0 レ
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...
Question 3 : Branch and Bound max 36a1282+8as s.t. 21i + 20r2 6xs 23 a e 10, 1]3 Write the LP Relaxation of this problem. 1. 2. What type of problem is this? (this type of problem has a particular name) Solve this problem by branch-and-bound, using the branching rule for binary variables of branching o 3. the most fractional variable. On the next page, write down the branch-and-bound tree you obtained. a. Each node should include the solution letter,...
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