Consider the following IP:
max z = 2x1-4x2
s.t
2x1 + x2 <= 5
-4x1 + 4x2 <= 5
x1,x2 >=0; x1,x2 integer
The optimal tableau for this IP's linear programming relaxation is given in Table 88. Use the cutting plane algorithm to find the optimal solution.
Original question is located in "Operation Research Applications and Alogrithms 4th edition" book by W.Winston. Topic: Cutting Plane Algorithm,Section 9.8. Page 549, PROBLEMS, Group A, 3rd question.
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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
Question 3: Identify which of LP problems (1)--(4) has (x1,x2) = (20,60) as its optimal solution. (1) min z = 50xı + 100X2 s.t. 7x1 + 2x2 > 28 2x1 + 12x2 > 24 X1, X2 > 0 (2) max z = 3x1 + 2x2 s.t. 2x1 + x2 < 100 X1 + x2 < 80 X1 <40 X1, X2 > 0 (3) min z = 3x1 + 5x2 s.t. 3x1 + 2x2 > 36 3x1 + 5x2 > 45...
Solve the following Integer Linear Programming Problem graphically using the method presented in class. Indicate whether problem is unbounded, infeasible and if an optimal solution exists, clearly state what the solution is. MAX Z = X1 + 2X2ST 4X1 + 6X2 ≤ 22 X1 + 5X2 ≤ 15 2X1 + X2 ≤ 9 X1, X2 ≥ 0 and X1 integer
same question just A through D steps
(A) Introduce slack, surplus, and artificial variables and form the modified problem. (B) Write the preliminary simplex tableau for the modified problem and find the initial simplex tableau. () Find the optimal solution of the modified problem by applying the simplex method to the initial simplex tableau. (D) Find the optimal solution of the original problem, it it exists. Maximize P-3xı + 5x2 subject to 2x1 + x2 58 X1 + X2 =...
Our final question is on a type of linear programming problem that we did not cover in lectures. Consider the following program:max z=3x1+5x2+2x3 s.t x1+2x2+2x3<=10 2x1+4x2+3x3<=15 0<=x1<=4<=x2<=3<=x3<=3 As you realize, the above program differs from the ones discussed in class in that each decision variable has an upper bound. How would you modify Simplex Method to solve this program? Find the solution of this problem
QUESTION 13 A company has decided to use 0-1 (binary) integer programming to help to make some investment decisions. There are three possible investment alternatives from which to choose, but if it is decided that a particular alternative is to be selected, the entire cost of that alternative will be incurred (i.e., it is impossible to build one-half of a factory). The integer programming model is as follows: Max 5000X1+7000X2+9000X3 S.t. X1+X2+X3<=2 (only 2 may be chosen) 25000X1+32000X2+29000X3<=62000 (budget limit) 16X1+14X2+19X3<=36 (resource...
QUESTION 13 A company has decided to use 0-1 (binary) integer programming to help to make some investment decisions. There are three possible investment alternatives from which to choose, but if it is decided that a particular alternative is to be selected, the entire cost of that alternative will be incurred (i.e., it is impossible to build one-half of a factory). The integer programming model is as follows: Max 5000X1+7000X2+9000X3 S.t. X1+X2+X3<=2 (only 2 may be chosen) 25000X1+32000X2+29000X3<=62000 (budget limit)...
I post this question but C, G, and H was not
answered...can I have an answer for them please as soon as
possible.
Interpreting an LP output after solving the problem using the software. The following linear programming problem has been solved using the software. Use the output to answer the questions below LINEAR PROGRAMMING PROBLEM: MAX 25X1+30X2+15X3 1) 4X1+5X2+8X3<1200 2) 9x1+15X2+3X3<1500 OPTIMAL SOLUTION: Objective Function Value- 4700.000 ariabl X1 x2 X3 0s 0.000 10.000 0.000 140.000 0.000 80.000 Less...
if you could only charge $18 for chairs, how is your optimal
solution change?
Variable Cells Allowable Increase Name Decision Variables X1 Decision Variables X2 Decision Variables X3 Final Value 2.0 0.0 8.0 Reduced Objective Cost Coefficient 0.0 60.0 -5.0 30.0 0.0 20.0 Allowable Decrease 20.0 4.0 5.0 1000000000000000000000000000000.0 2.5 5.0 Constraints Allowable Decrease Name Lumber bdft) Total Finishing (hrs) Total Carpentry (hrs) Total Tables demand (hrs) Final Value 24.0 20.0 8.0 0.0 Shadow Constraint Allowable Price R.H Side Increase...
Question 1 - Revised Simplex Algorithm 10 marks Suppose we are solving the following linear programming problem Subject to 8x1 + 12x2 + x3 15x2 + x4 3x1 + 6x2 + X5 -120 60 = 48 x1,x2,x3, x4,x5 2 0 Assume we have a current basis of x2,xz, x5. Demonstrate your understanding of the steps of the Revised Simplex Algorithm by answering the following: a) What is the basic feasible solution at this stage? What is the value of the...