Explanation Given: The minimization function: w = 3 y 1 + 2 y 2 Subjected to the system of inequality or constraints. 2 y 1 + 3 y 2 ≥ 60 y 1 + 4 y 2 ≥ 40 y 1 ≥ 0 , y 2 ≥ 0 , y 3 ≥ 0 Calculation: First, find the dual problem with maximization. Construct the argument matrix with coefficients of system of inequality and the coefficient of the minimization function. then, 2 3 60 1 4 40 3 2 0 The above argument matrix contains first two rows represent the coefficients of constraints and the last row shows the coefficient of the objective function. Now, find the transpose matrix of the argument matrix to find the dual problem. 2 1 3 3 4 2 60 40 0 Now, use ( x ) instead of ( y ) for dual problem, and the above transpose matrix shows that the first two rows represent the coefficients of constraints and the last row represents to coefficients of dual maximization problem. Then, The maximization function is z = 60 x 1 + 40 x 2 And inequalities equations are, 2 x 1 + x 2 ≤ 3 3 x 1 + 4 x 2 ≤ 2 x 1 ≥ 0 , x 2 ≥ 0 Now, use simplex method to solve the problem. The maximization function is: z = 60 x 1 + 40 x 2 Subjected to the system of inequality or constraints. 2 x 1 + x 2 ≤ 3 3 x 1 + 4 x 2 ≤ 2 x 1 ≥ 0 , x 2 ≥ 0 Now, use slack variables for converting the inequalities into equalities equations then the equations are, 2 x 1 + x 2 + s 1 = 3 3 x 1 + 4 x 2 + s 2 = 2 Form the simplex table, x 1 x 2 s 1 s 2 2 1 1 0 3 3 4 0 1 2 − 60 − 40 0 0 0 The last row of the above table shows the coefficients of the objective function and the row-1, row-2 show the coefficient of the constraints or system of inequality

12th Edition

ISBN: 9780134776323

Author: MULLINS

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

See similar textbooks

Concept explainers

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calcul…

Videos

Question

Chapter 7.6, Problem 26E

To determine

To calculate: The minimum value of the given function w=3y1+2y2 and the point at which the value of the function is minimum by using duality theorem.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 7.6, Problem 25E

Chapter 7.6, Problem 27E

Students have asked these similar questions

3. (a) Let A be an algebra. Define the notion of an A-module M. When is a module M a simple module? (b) State and prove Schur's Lemma for simple modules. (c) Let AM(K) and M = K" the natural A-module. (i) Show that M is a simple K-module. (ii) Prove that if ƒ € Endд(M) then ƒ can be written as f(m) = am, where a is a matrix in the centre of M, (K). [Recall that the centre, Z(M,(K)) == {a Mn(K) | ab M,,(K)}.] = ba for all bЄ (iii) Explain briefly why this means End₁(M) K, assuming that Z(M,,(K))~ K as K-algebras. Is this consistent with Schur's lemma?

(a) State, without proof, Cauchy's theorem, Cauchy's integral formula and Cauchy's integral formula for derivatives. Your answer should include all the conditions required for the results to hold. (8 marks) (b) Let U{z EC: |z| -1}. Let 12 be the triangular contour with vertices at 0, 2-2 and 2+2i, parametrized in the anticlockwise direction. Calculate dz. You must check the conditions of any results you use. (d) Let U C. Calculate Liz-1ym dz, (z - 1) 10 (5 marks) where 2 is the same as the previous part. You must check the conditions of any results you use. (4 marks)

(a) Suppose a function f: C→C has an isolated singularity at wЄ C. State what it means for this singularity to be a pole of order k. (2 marks) (b) Let f have a pole of order k at wЄ C. Prove that the residue of f at w is given by 1 res (f, w): = Z dk (k-1)! >wdzk−1 lim - [(z — w)* f(z)] . (5 marks) (c) Using the previous part, find the singularity of the function 9(z) = COS(πZ) e² (z - 1)²' classify it and calculate its residue. (5 marks) (d) Let g(x)=sin(211). Find the residue of g at z = 1. (3 marks) (e) Classify the singularity of cot(z) h(z) = Z at the origin. (5 marks)

Chapter 7 Solutions

EBK MATHEMATICS WITH APPLICATIONS IN TH

Ch. 7.1 - Checkpoint 1 Graph the given...Ch. 7.1 - Prob. 2CP Ch. 7.1 - Prob. 3CP Ch. 7.1 - Prob. 4CP Ch. 7.1 - Prob. 5CP Ch. 7.1 - Checkpoint 6 Graph the feasible region of the...Ch. 7.1 - Prob. 7CP Ch. 7.1 - Match the inequality with its graph, which is one...Ch. 7.1 - Match the inequality with its graph, which is one...Ch. 7.1 - Match the inequality with its graph, which is one...

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 minimum value of the given function w = 3 y 1 + 2 y 2 and the point at which the value of the function is minimum by using duality theorem.

Concept explainers

Videos

To calculate: The minimum value of the given function w=3y1+2y2 and the point at which the value of the function is minimum by using duality theorem.

Want to see the full answer?

Chapter 7 Solutions