Justify answer using complementary slackness and give optimal solution also to the dual aswell. Determine whether x' (;, ,) is an optimal solution to the following linearprogram:1 1 3213 2maximise 9x1 + 12x2 + 7x3subject to 3rı + 3r2 + lr3 < 4,201 + 3x2 + 2z < 5,31 + 4x2 + 2x3 <7,T1, 12, T3 20

Primal is MAX Zx = 9 x1 + 12 x2 + 7 x3 subject to 3 x1 + 3 x2 + x3 ≤ 4…

Answered: Determine whether x'= (,, ) is an…

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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Consider a set of 500 equations in 100 variables: Ax\le b, given by a_{i}^{T}x\le b_{i}. Suppose that these are not feasible, i.e., there is no solution that satisfies all of them. Show that in fact, there must be a subset of at most 101 which are not feasible. (Hint: Use duality and complementary slackness, E.g., what is the LP that finds the minimum value of slack s we have to put into Ax−1s≤b to make it feasible? The dual of such an LP could then be useful, and complementary slackness can relate variables and constraints between the two.).
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Which one is the optimal solution of given linear programming model? Max Z = X1 + X2 s.t. 8X1 + 6X2 12 X2 2 1 2X2 < 6 X1, X2 0. OA. X1= 9/4, X2 = 1, Max Z-13/4 O B. X1=3/ 2, X2 =1, Max Z-5/2 OC X1=6/8, X2 =3, Max Z-15/4 OD. X1=0, X2 = 3, Max Z=3 Seçimi Sıfırla
The oil company has three refineries located throughout the country with production capacity (120, 70 and 50) tons. Each day the company must supply its four customers with high purity gasoline with at least (60, 40, 30 and 110) tons. The transportation costs (in $) are given below. Obtain an initial basic feasible solution using Vogel's approximation model. Origin Destination A В 1 20 22 17 4 2 24 37 9. 7 3 32 37 20 15
A restaurant requires different numbers of full-time employees on different days of the week.Union rules state that each full-time employee must five consecutive days and then two daysoff. The management office wants to meet its daily requirements (Monday: 11, Tuesday: 16,Wednesday: 14, Thursday: 15, Friday: 18, Saturday: 19 and Sunday: 23) using only full-timeemployees. Formulate an LP that the restaurant can use to minimize the number of full timeemployees who must be hired
Point A// For the following LP model, determine the optimal solution using the .simplex method Max 50x₁ + 40x2 s.t. Assembly time Portable display Warehouse capacity 3x₁ + 5x₂ 150 1x₂20 8x₁ + 5x₂ ≤ 300 X₁, X₂ ≥ 0
• Consider the following LP: maximize 2x1 + 5x2 s.t. -x1 + 2x2 < 5 2x1 + 3x2 < 12 X1 + x2 2 -1 X1, X2 2 0 1. Write the dual problem. 2. Solve the optimal solution for the primal problem. 3. Find the optimal dual solutions by complementary slackness.
Justify your answer using complementary slackness and if given solution is optimal give the optimal solution to the dual too
șt. Consider the LP model below: Маx z 3D х, + X2 4x1 + x2 < 100 X1 + x2 < 80 X1 S 40 X1, X2 2 0 Find the values of all the variables at each basic solution. а. b. Find the optimal solution checking each of the basic feasible points (without drawing an isoprofit z line). С. Find the adjacent feasible points of optimal point.
Here is the original LP max z= 3x1 + 2x2 2x1 + *2 < 100 < 80 < 40 s.t. xi + x2 and the optimal tableau: S1 82 83 rhs 1 1 180 1 -1 2 60 -1 1 1 20 1 1 -1 0 20 Use decimals with no extra zero's: 1. What is the allowable increase for constraint 2 1 2. What is the allowable decrease for constraint 2 3. What is allowable increase for BV coefficient c2 4. What is allowable decrease for c2 5. Will {x2,s3, x1} be BV for a bfs if b2 is changed to 90 Y/N

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Determine whether x'= (,, ) is an optimal solution to the following linear program: 31 maximise 9x1 + 12x2 + 7r3 subject to 3rı + 3x2 + la3 < 4, 2a1 + 3r2 + 2r3 < 5, 311 + 4x2 + 23 <7, T1, T2, T3 2 0