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Problem 1. Consider the following problem etermine: (a) The maximum number of possible basic solu...
16.10 Consider the linear programming problem minimze -T subject to 1-2-1 T1,2 20 a. Write down the basic feasible solu...
16.10 Consider the linear programming problem minimze -T subject to 1-2-1 T1,2 20 a. Write down the basic feasible solution for z as a basic variable. b. Compute the canonical augmented matrix corresponding to the basis in part a c. If we apply the simplex algorithm to this problem, under what circum stance does it terminate? (In other words, which stopping criterion in the simplex algorithm is satisfied?) d. Show that in this problem, the objective function can take arbitrarily...
6. Consider the equation ſi 0 -17 |x=b, x>0. [1 1 1 Find all the basic...
6. Consider the equation ſi 0 -17 |x=b, x>0. [1 1 1 Find all the basic feasible solutions x for these values of b: []: [] [] 67 (-2): [ - ] [-] Draw a picture of the set of all b if x is feasible.
[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...
1. Consider the following problem Maximize Z = 2x2 subject to #1 2 (a) (points: 2)...
1. Consider the following problem Maximize Z = 2x2 subject to #1 2 (a) (points: 2) Plot the feasible region and circle all the CFP solutions (b) (points: 2.5) For each CFP solution, identify the pair of constraint boundary equations that it satisfies (c) (points: 2.5) For each CFP solution, use this pair of constraint boundary equations to solve algebraically for the values of 1 and r2 at the corner point (d) (points: 2.5) For each CFP solution, identify its...
Consider the following LP problem: Minimize Cost = 3x1 + 2x2 s.t. 1x1 + 2x2 ≤...
Consider the following LP problem: Minimize Cost = 3x1 + 2x2 s.t. 1x1 + 2x2 ≤ 12 2x1 + 3 x2 = 12 2 x1 + x2 ≥ 8 x1≥ 0, x2 ≥ 0 A) What is the optimal solution of this LP? Give an explanation. (4,0) (2,3) (0,8) (0,4) (0,6) (3,2) (12,0) B)Which of the following statements are correct for a linear programming which is feasible and not unbounded? 1)All of the above. 2)Only extreme points may be optimal....
Consider the following linear program: Max. 2A + 10B s.t. 3A ≤ 15 B ≤ 6...
Consider the following linear program: Max. 2A + 10B s.t. 3A ≤ 15 B ≤ 6 4A + 4B = 28 A, B ≥ 0 a.) Plot a graph that shows the feasible region for the problem b.) What are the extreme points of the feasible region
Consider the following linear program: Max 2A + 10B s.t. 3A ≤ 15 B ≤ 6...
Consider the following linear program: Max 2A + 10B s.t. 3A ≤ 15 B ≤ 6 4A + 4B = 28 A, B ≥ 0 a. draw graph that shows the feasible region for the problem b. What are the extreme points of the feasible region c. Draw graph that shows the optimal solution for the problem
Consider the following polynomial function. f(x) = – 8x10 + 2 (a) Determine the maximum number...
Consider the following polynomial function. f(x) = – 8x10 + 2 (a) Determine the maximum number of turning points of the graph of the function. (b) Determine the maximum number of real zeros of the function. Consider the following polynomial function. f(x) = 6x5 + 3x4 + 5 (a) Determine the maximum number of turning points of the graph of the function. turning point(s) (b) Determine the maximum number of real zeros of the function. Consider the following polynomial function....
Consider the following polynomial function. f(x) = – 8x10 + 2 (a) Determine the maximum number...
Consider the following polynomial function. f(x) = – 8x10 + 2 (a) Determine the maximum number of turning points of the graph of the function. (b) Determine the maximum number of real zeros of the function. Consider the following polynomial function. f(x) = 6x5 + 3x4 + 5 (a) Determine the maximum number of turning points of the graph of the function. turning point(s) (b) Determine the maximum number of real zeros of the function. Consider the following polynomial function....
Consider the following LP z= 2x1-x2 st s r 22 0 1. Prove the feasible region of the above LP is c...
Consider the following LP z= 2x1-x2 st s r 22 0 1. Prove the feasible region of the above LP is convex set. (Note: You could not prove using graphical representation) (2 points) 2. Find extreme directions of the feasible region. (2 points)
Consider the following LP z= 2x1-x2 st s r 22 0 1. Prove the feasible region of the above LP is convex set. (Note: You could not prove using graphical representation) (2 points) 2. Find extreme directions...
16.10 Consider the linear programming problem minimze -T subject to 1-2-1 T1,2 20 a. Write down the basic feasible solution for z as a basic variable. b. Compute the canonical augmented matrix corresponding to the basis in part a c. If we apply the simplex algorithm to this problem, under what circum stance does it terminate? (In other words, which stopping criterion in the simplex algorithm is satisfied?) d. Show that in this problem, the objective function can take arbitrarily...
6. Consider the equation ſi 0 -17 |x=b, x>0. [1 1 1 Find all the basic feasible solutions x for these values of b: []: [] [] 67 (-2): [ - ] [-] Draw a picture of the set of all b if x is feasible.
[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...
1. Consider the following problem Maximize Z = 2x2 subject to #1 2 (a) (points: 2) Plot the feasible region and circle all the CFP solutions (b) (points: 2.5) For each CFP solution, identify the pair of constraint boundary equations that it satisfies (c) (points: 2.5) For each CFP solution, use this pair of constraint boundary equations to solve algebraically for the values of 1 and r2 at the corner point (d) (points: 2.5) For each CFP solution, identify its...
Consider the following LP z= 2x1-x2 st s r 22 0 1. Prove the feasible region of the above LP is convex set. (Note: You could not prove using graphical representation) (2 points) 2. Find extreme directions of the feasible region. (2 points)
Consider the following LP z= 2x1-x2 st s r 22 0 1. Prove the feasible region of the above LP is convex set. (Note: You could not prove using graphical representation) (2 points) 2. Find extreme directions...
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