Concept explainers
Explanation of Solution
Solving the LP using simplex
Given,
Maximize
Subject to,
Converting to standard form:
As,
The standard form of LP problem becomes,
Maximize,
Subject to,
and
Converting LP to canonical form:
The LP is converted to canonical form by adding slack, surplus and artificial variables as appropriate. This is done as given below,
As the constraint “
For the constraint “
Thus the LP becomes,
Maximize
Subject to,
Iteration 1:
2 | 1 | -1 | 0 | 0 |
Min Ratio | |||
0 | 6 | (3) | 1 | -1 | 1 | 0 | ||
0 | 4 | 1 | 1 | -1 | 0 | 1 | ||
z=0 | 0 | 0 | 0 | 0 | 0 | |||
-1 | 1 | 0 | 0 |
Negative min
Minimum ratio is 2 and its row index is 1,
Want to see the full answer?
Check out a sample textbook solutionChapter 4 Solutions
Student Suite Cd-rom For Winston's Operations Research: Applications And Algorithms
- 4:using numpy to solve the system of linear equations as following x,y,z are variables. 3x+6y+7z = 10 2x+y+8y = 11 x+3y+7z = 22arrow_forwardWhat is the value of x after the 5th iteration of performing fixed-point iteration on the equation f(x) = x3 –x – 2? (Use the equation where the root converges and use an initial guess of 1) Group of answer choices 1.2599 1.5206 1.5158 1.5213arrow_forwardUse the simplex algorithm to solve a linear programming problem.arrow_forward
- Nonearrow_forward9. Solve the following system of equations by Gauss Elimination method (without pivoting): (v) 2x + 3y -z = 5 4x + 4y - 3z = 3 - 2x + 3y -z = 1 (v) x = 1, y = 2, z = 3 Ans. 10. Solve the following system of equations by Gauss Elimination method (without pivoting): (ui) 5xq − g + g = 10 2x₁ + 4x₂ = 12 *i+ Xg+5£g = −1 Ans. (ui) x1 = 23 9 " ₂x₂ = 31 18 , x3 == 19 18arrow_forwardA motorist found that the efficiency of her engine could be increased by adding lubricatingoil to fuel. She experimented with different amounts of lubricating oil and the data areAmount of lubricating oil (ml) 0 25 50 75 100 Efficiency (%) 60 70 75 81 84(a) (10 points) Obtain the least squares fit of a straight line to the amount of lubricatingoil.(b) (10 points) Test whether or not the slope β1 = 0. Take α = 0.05 as your level ofsignificance.(c) (10 points) Construct a 90% confidence interval on the mean response at x0 = 10 ml.(d) (10 points) Give a point estimate of the mean engine efficiency when the amount oflubricating oil is 450 ml.(e) (10 points) What additional danger is there when using your estimate in part (d)?arrow_forward
- dy 5 Find the general solution of the differential equation: dt t Use lower case c for constant in answer. y(t) = P 7 esc = 1 9 a @ 2 W S # 3 e d $ 4 r f % 5 rt וום 6 g y & 087 O h U 水 8 0 ( · y = t5. 9 k O O Farrow_forwardUse any programming language for the following: Machine Exercise: a. Make an Algorithm for solving systems of linear algebraic equations using the methods below: 1.) Gauss elimination 2.) LU decomposition method (any one of the following) • Doolittle's decomposition • Crout's decomposition Cholesky's decomposition 3.) Iterative methods (any one of the following) Gauss-Jacobi Gauss-Seidel • Successive Relaxation Conjugate Gradient b. Write a program for solving the system Ax = b by 1.) Gaussian elimination algorithm 2.) LU decomposition methods (any one of the three) %3D • Doolittle's decomposition • Crout's decomposition Cholesky's decompositionarrow_forward- The bucket has a weight of 400 N and is being hoisted using three springs, each having an unstretched length of 6 = 0.45 m and stiffness of k = 800 N/m. Determine the vertical distance d from the rim to point A for equilibrium. 400 N D. 120 120° 0.45 m 120° B 3d EF, = 0; 400 – F = 0 d² + (0.45)² 400 N 3d [800 Jd² + (0.45)² -0.45)] = 0 400 d² + (4.5)² |d² + (0.45)² -0.45) = 0.16667 0.45 m d² + (4.5)² d d² + (0.45)² -0.45 d = 0.16667 Jd² + (0.45)² Va? + (0.45)² (d– 0.16667) = 0.45 0.45 m d [d² + (0.45)*] [d° – 2d(0.16667) + (0.16667)°] = (0.45)² d² d* – 0.33334 d + 0.027779 d – 0.0675 d + 0.0056252 = 0 120° 0.45 m d = 0.502 m Ansarrow_forward
- What is the value of x in the 4th iteration of performing fixed-point iteration on the equation f(x) = x3 –x – 2? (Use the equation where the root converges and use an initial guess of 1)Group of answer choices 1.5158 1.5288 1.2599 1.5211arrow_forwardThe initial tableau of a linear programming problem is given. Use the simplex method to solve the problem. X2 X3 6 2 1 2 - 1 - 3 X1 1 3 -5 S₁ 1 0 0 S2 0 1 0 Z 0 0 1 18 39 The maximum is | when x₁ = ₁X₂ = ₁ x3 =₁ $₁=₁ and $₂ = - X3 (Type integers or simplified fractions.)arrow_forwardSolve the following using deetailed explanationarrow_forward
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole