Explanation Given Information: The provided matrix is: Minimize c = 2 x + y + 2 z Subject to 3 x + 2 y + z ≥ 100 , 2 x + y + 3 z ≥ 200 and x ≥ 0 , y ≥ 0 , z ≥ 0 Formula used: Solving the given Dual problem by the following steps: Step 1) Represent the problem as a matrix. Step 2) Take the transpose of the matrix. Step 3) Write down the dual, which is the LP problem corresponding to the new matrix. If the original problem was a maximization problem, its dual will be a minimization problem, and vice versa. Fundamental Theorem of duality as: If an LP problem has a optimal solution, then so does its dual. Moreover, the primal problem and the dual problem have the same optimal value for their objective functions. Contained in the final tableau of the simplex method applied to an LP problem is the solution to its dual problem: It is given by the bottom entries in the column associated with the slack variables, divided by the entry under the objective variable. Calculation: Consider the provided matrix is: Minimize c = 2 x + y + 2 z Subject to 3 x + 2 y + z ≥ 100 , 2 x + y + 3 z ≥ 200 and x ≥ 0 , y ≥ 0 , z ≥ 0 Step 1) Represent the problem as a matrix. [ 3 2 1 2 1 3 2 1 2 100 200 0 ] Step 2) Take the transpose of the matrix. [ 3 2 2 2 1 1 1 3 2 100 200 0 ] Step 3) Write down the dual, which is the LP problem corresponding to the new matrix. If the original problem was a maximization problem, its dual will be a minimization problem, and vice versa. Maximize p = 100 x + 200 y Subject to 3 x + 2 y + z ≥ 100 , 2 x + y + 3 z ≥ 200 and x ≥ 0 , y ≥ 0 , z ≥ 0 Solve the dual problem as: x y s t u p s 3 2 1 0 0 0 2 t 2 1 0 1 0 0 1 u 1 3 0 0 1

7th Edition

ISBN: 9781337280426

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

See similar textbooks

Videos

Question

Chapter 5, Problem 20RE

To determine

To calculate: The linear programming problem by the method of duality.

Minimize c=2x+y+2z

Subject to 3x+2y+z≥100,2x+y+3z≥200 and x≥0,y≥0,z≥0

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 5, Problem 19RE

Chapter 5, Problem 21RE

Students have asked these similar questions

Calculs Insights πT | cos x |³ dx 59 2

2. Consider the ODE u' = ƒ (u) = u² + r where r is a parameter that can take the values r = −1, −0.5, -0.1, 0.1. For each value of r: (a) Sketch ƒ(u) = u² + r and determine the equilibrium points. (b) Draw the phase line. (d) Determine the stability of the equilibrium points. (d) Plot the direction field and some sample solutions,i.e., u(t) (e) Describe how location of the equilibrium points and their stability change as you increase the parameter r. (f) Using the matlab program phaseline.m generate a solution for each value of r and the initial condition u(0) = 0.9. Print and turn in your result for r = −1. Do not forget to add a figure caption. (g) In the matlab program phaseline.m set the initial condition to u(0) = 1.1 and simulate the ode over the time interval t = [0, 10] for different values of r. What happens? Why? You do not need to turn in a plot for (g), just describe what happens.

The following are suggested designs for group sequential studies. Using PROCSEQDESIGN, provide the following for the design O’Brien Fleming and Pocock.• The critical boundary values for each analysis of the data• The expected sample sizes at each interim analysisAssume the standardized Z score method for calculating boundaries.Investigators are evaluating the success rate of a novel drug for treating a certain type ofbacterial wound infection. Since no existing treatment exists, they have planned a one-armstudy. They wish to test whether the success rate of the drug is better than 50%, whichthey have defined as the null success rate. Preliminary testing has estimated the successrate of the drug at 55%. The investigators are eager to get the drug into production andwould like to plan for 9 interim analyses (10 analyzes in total) of the data. Assume thesignificance level is 5% and power is 90%.Besides, draw a combined boundary plot (OBF, POC, and HP)

Chapter 5 Solutions

Finite Mathematics

Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - Prob. 6E Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - Prob. 9E Ch. 5.1 - In Exercises 1-26, sketch the region that...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The linear programming problem by the method of duality. Minimize c = 2 x + y + 2 z Subject to 3 x + 2 y + z ≥ 100 , 2 x + y + 3 z ≥ 200 and x ≥ 0 , y ≥ 0 , z ≥ 0

Solution Summary: The author explains the formula used to solve the linear programming problem by the method of duality.

Videos

To calculate: The linear programming problem by the method of duality.

Minimize c=2x+y+2z

Subject to 3x+2y+z≥100,2x+y+3z≥200 and x≥0,y≥0,z≥0

Want to see the full answer?

Chapter 5 Solutions

The linear programming problem by the method of duality. Minimize c = 2 x + y + 2 z Subject to 3 x + 2 y + z ≥ 100 , 2 x + y + 3 z ≥ 200 and x ≥ 0 , y ≥ 0 , z ≥ 0

Solution Summary: The author explains the formula used to solve the linear programming problem by the method of duality.

Videos

To calculate: The linear programming problem by the method of duality. Minimize c=2x+y+2z Subject to 3x+2y+z≥100,2x+y+3z≥200 and x≥0,y≥0,z≥0

Want to see the full answer?

Chapter 5 Solutions

To calculate: The linear programming problem by the method of duality.

Minimize c=2x+y+2z

Subject to 3x+2y+z≥100,2x+y+3z≥200 and x≥0,y≥0,z≥0