Consider the following minimum problem: Minimize: C = 22 Subject to the constraints: 1 +5:03 >...
Consider the following minimum problem: Minimize: C=2.01 +32 Subject to the constraints: 5.21 +22 > 9 201 + 2.02 > 10 > 0 * > 0 Write the dual problem for the above minimum problem by selecting the appropriate number for each blank box shown below (Do not solve the dual problem). P= (Select) Yi+ (Select) Y2 (Select) 31+ [ Select) y2 <2 (Select) Y1+ Select) y2 <1 yı > 0 y2 > 0
10. What is the dual of the following problem: Minimize x1 + x2, subject to xi 20, x2 > 0, 2xı > 4, x1 + 3x2 > 11? Find the solution to both this problem and its dual, and verify that minimum equals maximum.
Use the simplex method and the Duality Principle to solve the following minimum problem: Minimize: C = 2001 +622 Subject to the constraints: - 201 +3.02 > 0 31 +3:02 > 9 C1 0 22 > 0 and using your final tableau answer the questions below by entering the correct answer in each blank box. Please enter fractions as 3/5, -4/7, and so on. 11 12 C=
1. The following linear programming problem is given: 1(x)-9z1 + 5x2 + 5x3 → maximize under constraints: 22 S 5 9r1 +42 +4z354 1 1-229 1 20,2 20 (a) Write it is the standard form. (b) Find a vertex of the constraint set in the standard form. (c) Write the dual problem. (d) Solve the dual problem. (e) Solve the original problem. 1. The following linear programming problem is given: 1(x)-9z1 + 5x2 + 5x3 → maximize under constraints: 22...
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...
Operations Research Problem 2. Consider the following program: Minimize 2 22 subject to+ x2 s2 2x1 + 3x2 21 xi r2 21 Please solve the problem graphically and perform sensitivity analysis (along the lines of Supple- mentary text): (a) determine the amount of slack (or unused surplus) in the constraints at the optimal solu tion; )etie shadow prices/reduced s ociated with the constraints (c) for the binding constraints, determine the ranges for the right-hand side coefficients such that the constraints...
Consider the following LP problem. minimize 3:01 +4.c3 subject to 2:01 + x3 - I3 < -2 21 +3.02 – 5x3 = 7 21 <0,22 > 0, 03 free Which of the LP problem below is its dual problem? maximize -2p1 + 7p2 subject to 2p. + P23 1 + 3p2 50 -P1 - 5p2 = 4 Vi < 0,2 > 0 maximize --2p1 + 702 subject to 2p. + P23 1 + 3p2 50 -P1 - 5p2 = 4...
Use the simplex method and the Duality Principle to solve the following minimum problem: Minimize: C = 3.21 +8:02 Subject to the constraints: 2:41 + 7.02 > 9 21 +222 > 4 0 32 > 0 21 and using your final tableau answer the questions below by entering the correct answer in each blank box. Please enter fractions as 3/5, -4/7, and so on. C1 = C=
In the simplex method, which of the following is considered a Standard Maximum problem? (Please select one answer). O Maximize: Z = 601 +8.02 Subject to the following constraints: 5x + 10x2 < 60 401 + 402 <-40 X>0; 202 > 0 Maximize: P = -1 +232 + 3003 Subject to the following constraints: 21 + 2.02 + 2003 < -20 5.01 2x2 + 4.03 <15 2.01 + 2x2 + 4.03 < 23 X>0 220; 203 > 0 Maximize: P=40:21...
Consider the following Linear Problem Minimize 2x1 + 2x2 equation (1) subject to: x1 + x2 >= 6 equation (2) x1 - 2x2 >= -18 equation (3) x1>= 0 equation (4) x2 >= 0 equation (5) 13. What is the feasible region for Constraint number 1, Please consider the Non-negativity constraints. 14. What is the feasible region for Constraint number 2, Please consider the Non-negativity constraints. 15. Illustrate (draw) contraint 1 and 2 in a same graph and find interception...