Minimize Z = 0.2x, + 0.1x, + 0.3x,Subject to constraint0. 5x, + 0.2x, + 0.7x, = 0.4200. 3x, + 0.2x2 + 0.5x, 2 0.280) Write second initial basic solution of the primal problem using M-Method.(1) Solve the dual from optimal Primal table caleulated in (i).Maximum file size: 25MB, maximum

1) The problem is converted to canonical form by adding slack, surplus, and artificial variables as…

Answered: Minimize Z = 0.2x, + 0.1x, + 0.3x,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Solve this LP max z = 3x1 + 2x2 + 2.5x3 8.t.. has optimal tableau So B = 1 + x + 2x3 201 + 2x3 1, 2, 3 > 0 13 23 and B-¹ and using B-¹ and B-¹ cay formulas the missing values in optimal tableau are €3 =■; €8₂ =0; 5₁=;5₂ = <4 ≤6 and cay = [00] and the optimal solution for z is z = Now find the maximum amount A = z 01 1 0 0 0 0 1 2 0 1 0 rhs 23 81 82 C3 čai 1/2 ā13 1 -1/2 ā23 0 1/2 5₂ that the value of c3 can be increased so that the optimal BV remains optimal.
4- Solve the following problem by the two-phase simplex method: Min x₁ + 3x2 - X3 s.t 2x₁ + x₂ + x3 ≥ 3 -x₂ + 5x₂ + x3 ≤ 4 ≥2 -x₁ + x₂ X1, X2, X3 20
[3.6] Consider the following problem: Maximize - 3x₁ subject to -X1 + a. b. 2x2 2.x1 + 3x2 X1 x2 X₂ VIVINA ♡ N -com 1 6 0 24/3. S Solve the problem graphically. Set up the problem in tableau form for the simplex method, and obtain an initial basic feasible solution.
1. Use the simplex method in tabular form to solve the problem: Maximize Z= 2x1 + 4x2 + 3x3 subject to and 21 +372 +2r3 ≤ 30 21+22+13 ≤ 24 3x1 +52 + 3x3 ≤60 2120, 220, 23 20.
Perform the indicated operation. (30 3-j19) (j2-1)
2 2. (10 pts) Consider the product XY where x and y are positive numbers which 2, must sum to six (6). Find the maximum value of xy under this contraint. a. Write the constraint equation. b. Use the equation in (a) to write the objective function in terms of the variable x. C. Apply the necessary calculus to solve the problem. Be sure to include a verification step, i.e. why your solution is the maximum. Also, give the maximum value.
A manufacturer produces three products: Product A, Product B and Product C. Tobe able to produce each product he uses a combination of three distinct inputsnamely Input I, Input II and Input III the supply of which is currently at 730, 350and 350 units respectively. Each unit of Product A requires 6 units of Input I, 3units of Input II and 4 units of Input III to be produced. Similarly, each unit ofProduct B requires 8 units of Input 1 and 4 units of Input II while Product C uses 5units of Input I, 1 unit of Input II and 3 units of Input III.(i) Let a, b and c represent the number of units produced of Products A, B and Crespectively. The manufacturer must decide what quantity of each product toproduce so that his entire supply of inputs is utilized. Formulate his/herdecision in the form of a system of three linear equations in the variables a, band c. [3 marks](ii) Rewrite the above system of linear equations in the matrix form Ax = b. [2 marks](iii) Hence or otherwise, determine how…
Can you answer this in pencil and paper?
4- Solve the following problem by the two-phase simplex method: Min x₂ + 3x₂ - X3 s.t 2x₁ + x₂ + x3 ≥ 3 -x₂ + 5x₂ + x3 ≤ 4 -x₁ + x₂ 2 X1, X2, X3 20
A and B can do a piece of work in 12 days; B and C can do it in 15 days while C and A can finish it in 20 days. In how many days will A,B,C finish it, working togeteher? In hpw many days will each one of them finish it, working alone?
3. SOLVE USING TWO-PHASE METHOD Minimize x₁ - -3x3 subject to x₁ + 2x₂ X3 ≤6 x₂ + 3x3 = 3 X1, X2, X30
Question 29 Maximize 2x1 + 4x2 subject to x1 + 3x₂ �� 12 2x1 + x₂ ≤ 14 120 and ₂ > 0 Using simplex method by introducing slack variables 3 and 4, and M = 2x1 + 4x2, now the inequalities are changed to equations x1 + 3x2 + x3 = 12 (1) 2x1 + x₂ + x4 = 14 (2) 2x14x2 M = 0 (3) To bring 1 and 2 into the solution, which one (1 or 2) is firstly brought into the solution and which equation is used as the pivot equation. O1 and (2) O #2 and (3) O2 and (2) O #1 and (1) O2 and (1)

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Minimize Z = 0.2x, + 0.1x, + 0.3x, Subject to constraint 0. 5x, + 0.2x, + 0.7x, = 0.420 0. 3x, + 0.2x, + 0.5x, 2 0.280 X. X 20. ) Write second initial basic solution of the primal problem using M-Method. (1) Solve the dual from optimal Primal table calenlated in (i).