Problem 4: Consider the tabulated standard-form LP starting with X1 and X2 basic. Please apply the...

Problem 4: Consider the tabulated standard-form LP starting with X₁ and X₂ basic. Please apply the revised simplex method and solve the LP.

Note: in each iteration determine Matrix A, B, E, V, C, and the improving direction!

	X₁	X₂	X₃	X₄	X₅
Min C	5	4	3	2	16	b
A	2	0	1	0	6	8
A	0	1	1	2	3	12

Expert Solution

Colby Messinger answered 3 years ago

You are given the following LP model in algebraic form, with x1 and x2 as the...

You are given the following LP model in algebraic form, with x1 and x2 as the decision variables: Minimize Cost = 40x1 + 50x2 Subject to Constraint 1: 2x1 + 3x2 >= 30, Constraint 2: x1 + x2 >= 12, Constraint 3: 2x1 + x2 >= 20, and x1 >=0, x2 >= 0. Use the graphical method to solve this model. How does the optimal solution change if the objective function is changed to Cost = 40x1...

consider the following LP a. put the problem into standard form, using slack, excess, and artificial...

consider the following LP a. put the problem into standard form, using slack, excess, and artificial variables b. solve the associated LP of phase I c. is w'=0, proceed to phase 2 and solve the original LP. show all of the work. max z=x1-x2+3x3 S.T. x1+x2<=20 x2+x3>=10 x1+x3=5 x1,x2>=0

Consider the following LP model.Max Z = 3x1 - 4x2 + x3 subject to x1 + x2 +...

Consider the following LP model.Max Z = 3x1 - 4x2 + x3 subject to x1 + x2 + x3 >= 9 2x1 + x2 + x3<= 12 x1 + x2 = 5 x1, x2, x3 >= 0 Change it to standard form. Obtain all the basic solutions and indicate which ones are basic feasible solutions and write down the corresponding corner points. For each basic solution, you have to obtain the values of all the variables. Obtain the solution of the LP...

Consider the problem maximize Z = 5 x1 + 3 x2 + 2 x3 + 4...

Consider the problem maximize Z = 5 x1 + 3 x2 + 2 x3 + 4 x4 subject to 5 x1 + x2 + x3 + 8 x4 = 10 2 x1 + 4 x2 + 3 x3 + 2 x4 = 10 X j > 0, j=1,2,3,4 (a) Make the necessary row reductions to have the tableau ready for iteration 0. On this tableau identify the corresponding initial (artificial) basic feasible solution. Also, identify the initial entering and...

Consider the following linear programming problem. min −x1 + 4x2 subject to: • x1 + x2...

Consider the following linear programming problem. min −x1 + 4x2 subject to: • x1 + x2 ≥ 1 • 3x1 + x2 ≤ .5 • x1, x2 ≥ 0 Formulate the dual of this problem.

Solve the following LP problem using graphical solution method. MAX: 5 X1 + 3 X2 Subject...

Solve the following LP problem using graphical solution method. MAX: 5 X1 + 3 X2 Subject to: 2 X1 − 1 X2 ≤ 2 6 X1 + 6 X2 ≥ 12 1 X1 + 3 X2 ≤ 5 X1, X2 ≥ 0

Consider a sequence of random variables X0, X1, X2, X3, . . . which form a...

Consider a sequence of random variables X0, X1, X2, X3, . . . which form a Markov chain. (a) Define the Markov property for this Markov chain both in words and using a mathematical formula. (b) When is a Markov chain irreducible? (c) Give the definition for an ergodic state.

Consider the following three consumption bundles (X1,X2)=(10,10) ; (X1,X2)=(15,10) ; (X1,X2)=(3000,8).

Answer each of the following statements True/False/Uncertain. Give a full explanation of your answer including graphs where appropriate. (When in doubt, always include a fully labeled graph.)A) Consider the following three consumption bundles (X1,X2)=(10,10) ; (X1,X2)=(15,10) ; (X1,X2)=(3000,8). Non-satiation implies that (15,10) is preferred to (10,10) but does not imply that (3000,8) is preferred to (10,10).B) It is not theoretically possible for two indifference curves to cross if the preference relations they are based on satisfy the assumptions of completeness,...

consider the linear programming problem maximize z = x1 +x2 subjected tp x1 + 3x2 >=...

consider the linear programming problem maximize z = x1 +x2 subjected tp x1 + 3x2 >= 15 2x1 + x2 >= 10 x1 + 2x2 <=40 3x1 + x2 <= 60 x1 >= 0, x2>= 0 solve using the revised simplex method and comment on any special charateristics of the optimal soultion. sketch the feasible region for the problem as stated above and show on the figure the solutions at the various iterations

Find the Dual of the following LP max z = 4x1 − x2 + 2x3 x1...

Find the Dual of the following LP max z = 4x1 − x2 + 2x3 x1 + x2 ≤ 5 2x1 + x2 ≤ 7 2x2 + x3 ≥ 6 x1 + x3 = 4 x1 ≥ 0, x2, x3 free

Question