In Problems 13-20,
(A) Form the dual problem.
(B) Find the solution to the original problem by applying the simplex method to the dual problem.
Want to see the full answer?
Check out a sample textbook solutionChapter 6 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (4th Edition)
Basic Business Statistics, Student Value Edition
Elementary Statistics: Picturing the World (7th Edition)
Elementary Statistics
Algebra and Trigonometry (6th Edition)
College Algebra with Modeling & Visualization (5th Edition)
- Use the simplex method to solve the following. z = 3x₁ + 3x₂ - 6x3 5x₁ + 5x₂ - 10x3 ≤ 75 6x₁ + 6x₂ + 12x3 ≤ 104 X₁ ≥ 0, X₂ ≥0, X3 ≥ 0. Maximize subject to Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. Treating x₂ as a nonbasic variable, the maximum is x₁ =₁ X₂ = ‚ X3: S₁ = 0 and $₂ B. There is no maximum solution for this problem. whenarrow_forwardSolve the following problem using the standard simplex method. Minimize C =-4x - 7y Subject to 6.x+ 2y 0, y > 0arrow_forward1 Maximize Z = x, + 2r, + 4x3, subject to 3x, + x2+5xr, s 10 x,+4x, + r, s 8 2x + 2x, s 7 and Using the simplex method, the optimal value of the objective of the following problem is:arrow_forward
- What is considered "the best of both worlds" for working with non-linear problems in Excel? -GRG Multi-start -Simplex LP -Evolutionary -GRG Nonlineararrow_forwardb) Consider the following simplex problems: Max. Z=3X1 + 2X2 (Objective Function) Subject to: -XI + 2X2 <4 3X1+ 2X2 < 14 -X1 - X2 53 Where XI, X2 20 (non – negativity) Solve this problem using both graphical and simplex models to find out the optimal solution points and state your conclusion from both techniques.arrow_forwardThe formulation of a non-linear problem is as follows: Max f = (10 + 7x1 - x1² ) + (10 + x2 - x22 ) + (20 %3D + 3x3 - x3) subject to: X1 + X2 + X3 = 8 {x} > O Select the Recursive Equation needed to solve stage 2 (corresponding to the variable x2), using Dynamic Programming to solve the problem. a) f2(S2,x2) = (10 + x2 - X2² ) + f3^( x2 ) b) f2(S2,x2) = (10 + x2 - x22 ) + f3° ( 8 - x1) * c) f2(S2,x2) = (10 + x2 - X2 ) + f3"( 8 - x2 ) d) f2(S2,x2) = (10 + x2 - x2 ) + f3"(8 - x1 - x2 )arrow_forward
- In this problem we want to understand how the simplex method deals with an LP problem having an infinite number of solutions. Solve: Maximize z = 2.x1 + 4x2 subject to x1 + 2x2 0. You will get an optimal solution by doing just one iteration. But there could be more solutions as the objective function has the same slope as the line determined by the second constraint. If you did not know that, what features in the tableau would have signalled this possibility? State your idea as a rule that checks the final tableau to determine if an infinite number of op solutions is possible. Give a very brief explanation to justify why your rule should work. mal Using your rule, do one more iteration to obtain a second optimal solution.arrow_forwardFind the optimal value of the objective function for the LP problem (without using simplex method to solve the primal and the dual problem) Min z=10x, + 4x, +5x, subject to 5x, - 7x, +3x, 2 50 X,, X,, X, 20 Hint: Inspect the dual problem.arrow_forwardSolve the following using Simplex Method. 1. A factory makes three types of chairs, A, B, and C. The factory makes a profit ci P200 on chair A, P300 on chair B, and P400 on chair C. Chair A requires 30 man-hours, chair B requires 20, and chair C requires 10. Chair A needs 2m2 of wood, chair needs 5m2, and chair C needs 3m2. Given 100 man-hours and 15m2 of wood per week, how many chairs of each type should be made each week to maximize profit? 2. Maximize Z = 8x +6 x Subject to: 10x,+ X2s 12 2xi+ 5 x2s 16 X120 INHarrow_forward
- Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill EducationMathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
- Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSONDiscrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education