5-18 Consider the linear program max 4y1 + 5y2 s.t. -y1 + y2 ≤ 4 y1 - y2 ≤ 10 y1, y2 0 (a) Show graphically that the model is unbounded. (b) Add slacks y3 and y4 to place the model in standard form. (c) Starting with all slacks basic, apply rudimentary simplex Algorithm 5A to establish that the original model is unbounded.

5-18 Consider the linear program max 4y1 + 5y2 s.t. -y1 + y2 ≤ 4 y1 - y2 ≤ 10 y1, y2 0 (a) Show graphically that the model is unbounded. (b) Add slacks y3 and y4 to place the model in standard form. (c) Starting with all slacks basic, apply rudimentary simplex Algorithm 5A to establish that the original model is unbounded.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 53EQ

See similar textbooks

Related questions

Q: 1 1 2 4 1 Determent if the Rre linearly independent or linear dependent. If It is linear dependent,…

Q: 123 five to base nine

A: 123five = (1×5^2)+(2×5)+(3×5^0) =25 +10 +3 =38

Q: This extreme value problem has a solution with both a maximum value and a minimum value. Use…

Q: Determine whether the statement is true or false. If the statement is false, make the necessary…

A: Given Statement: 'An equivalent form for a conditional statement is obtained by reversing and…

Q: d4 [Pn(x)]Pn(x)dx. -1 dr

A: We have to evaluate : ∫-11d4dx4PnxPnx dx Prerequisite : 1. Pn1=1 2. Pn-1=-1n 3. Pn11=nn+12 4.…

Q: Homogeneous Equations Obtain the family of solution of the equation 3xydx+(x2+y2)dy=0

Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral…

A: Given ∫02ex4+x2dx, n=10

Q: 5. Simplify the expression using a Pythagorean identity: 6. Simplify the expression using a…

Q: Consider the limits of f at infinity. lim f(x) = 0 x18 lim f(x) = 2 Select all possible graphs of f.…

A: I am taking options as followingA BC DEIn option Alimx→∞f(x)=limx→-∞f(x)=0This option is…

Q: Solve the separable differential equation Subject to the initial condition: y(0) = 9. y = 11x -…

Q: Obtain the particular solution when x = -1 and y = 0 1 (2x + 3)dy = ydx + (2x + 3) dx

Q: Solve the given differential equation by separation of variables. dy dx = sin(6x)

Q: e some detailed solution and please do not copy other's work,thanks!! 2. Let S S CRN. Show that a(S₁…

Q: n gent

Q: disprove the given statement. 10. The number n is an even integer if and only if n 3 + 13 is odd.…

A: Proof of the statements

Q: Solve: y' + 7y +9y' +9y=0 y(x)

Q: How many 8-digit binary strings end in 1 or have exactly four 1's?

Q: K4,4 Multiple Choice . . . . ܩ ܦ ܕ ܕ . ܘ

Q: II. Determine the point(s) of intersection, m, and m₂, and the angle(s) of intersection of the given…

Q: Consider the following matrices: A = V₁ = 5² TNN V3 = For each of the following matrices, determine…

Q: 3(x + 1)(x-4) (x-1)² Determine the equation of the horizontal asymptote of f(x) (if any). Explain…

A: Given function is fx=3x+1x−4x−12. It can be written as follows fx=3x2−9x−12x2−2x+1 First we have to…

Q: A scale drawing of a football field has a scale of 1 inch to 40 feet. The area of the scale drawing…

Q: Examples. Justify your answers briefly. (b) Give an example of a real function that is increasing on…

Q: Note: To create a wire, drag from the output of a component to the input of another component.…

Q: Solve the linear programming problem by the method of corners. Minimize C = 7x + 6y subject to…

Q: The Jesaki research department established the following price-supply function for widgets: q(x) =…

A: We will use given price supply and price demand functions to compute equilibrium price.

Q: An account have the nominal rate of 5.4% find the effective annual yield would round to the…

A: An account have the nominal rate of 5.4% We have to find the effective annual yield for quarterly…

Q: If p is a prime, prove that xp-1 - xp-2 + xp-3 - ... - x + 1 is irreducibleover Q.

Q: State the order of the given ordinary differential equation. (sin 0)y"" - (cos 0)y' = 5 Determine…

Q: Show that if A and B are n x n matrices then N(A-B) = R" if and only if A = B.

Q: 1. Find the local maximum and minimum values and saddle point(s) of the function. If you have…

Q: merchant surveyed 540 people to determine the way they learned about an upcoming sale. The survey…

Q: Solve the system of equations in three variables. 2x+y 2z=-1 3x - 3y-z = 5 z-2y+3z=6

Q: Type the equation in the form y= A sin (ox) or y= A cos (@x). y =

Q: use Equation in the picture to verify that λ and v are an eigenvalue/eigenvector pair for the given…

A: Eigen value and eigen vectors of the matrix

Q: 15. (a) Find the solution of the differential equation x(x + 1) dy + xy = 1. dx (b) Give the largest…

Q: Find the general solution of the given differential equation. y'''-3y''+3y'-y=0 If using a…

Q: B. In a certain school, 50 students in a certain class were as follows: 30 enrolled in Algebra 25…

Q: How many 10-digit binary strings begin in 1 or end in 1?

Q: (b) (c) (d) (e) dy=3x²(y-1) dx dy_y+2 = dx x+1 dy dx -+e*y² = 0 dy dx -= cos x tan y hotnes

Q: How would I state the Principle of Mathematical Induction for P(b), b∈ N with only math symbols (no…

Q: Complete the truth table for the given statement by filling in the required columns. -pv-q Pq Р TT T…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Using focused laser light, optical tweezers can apply a force of about 13 pN to a 1.6 μm diameter…

Q: Use secant method in finding the root of Consider the given initial values: x_₁ = 0, f(x)=-1+5.5x -…

Q: Use the formula of the Laplace Transform to get the L [t^n]

Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the…

A: A vector is a quantity that has both magnitude and direction. In general, vectors are represented as…

Q: When the forgetfulness of an individual is taken into account, the speed with which he memorizes is…

Q: The system of equations Ax = 0 has solutions that generate a vector subspace V. i. Solve the system,…

Q: D. If the original inequality of interest were instead 0 < |x − 2| < 3, exactly one real number must…

Q: dy = sinx;y=1 when = dx 2 dy_cos x d.x = y dy (e) (1-x²)= y(1+x²); y = 1 when x=0 dx (c) e. (d) el…

Concept explainers

Optimization Models

Optimization models are mathematical models that help organizations determine the best way to allocate scarce resources to achieve specific objectives. These models can be used to solve a wide variety of problems, from finding the most efficient route for a delivery truck to determining the optimal mix of products to stock in a store.

Question

5-18 Consider the linear program
max 4y1 + 5y2
s.t. -y1 + y2 ≤ 4
y1 - y2 ≤ 10
y1, y2 0
(a) Show graphically that the model is
unbounded.
(b) Add slacks y3 and y4 to place the model
in standard form.
(c) Starting with all slacks basic, apply rudimentary simplex Algorithm 5A to establish that the original model is unbounded.
5-19 Do Exercise 5-18 for the LP
min -10y1 + y2
s.t. -5y1 + 3y2 ≤ 15
3y1 - 5y2 ≤ 8
y1, y2 ≥0

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Trending now

This is a popular solution!

Step by step

Solved in 6 steps with 5 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Optimization models$

Learn more about

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

Similar questions

By employing the Adams Fourth-Order Predictor-Corrector algorithm with the step size h=0.2, find the numerical solution of the following problem at t = 0.4; y^ prime =t^ 2 -2e^ -2t; y(0) = 1 , The true solution of this problem is 0 <= t <= 1 , y(t) = (t ^ 3)/3 + e ^ (- 2t) * C * o * m * p * c numerical result with the actual solution at this point. the obtained
(a) Consider matrices A, U, and V , where A is an invertible n × n matrix, and U and V are n × k matrices with rank k < n. Prove the Sherman–Morrison–Woodbury formula, i.e., that T = I − (V^T) (A^−1)U is nonsingular if and only ifA – UV^T is nonsingular, in which case (A – UV^T)^−1 = (A^−1)−( A^−1)(UT^−1)(V^T)A^−1. (b) Suppose you have a fast algorithm for solving Ax = b (for example, using an LU factorisation of A). Show how to build a fast algorithm for solving Bx = c, where B = A – UV^T.
Solve the following mixed integer programming problem by using Branch and Bound algorithm. Maximize Z = x1 +x2 Subjected to 2x1 + 5x2 ≤ 1 6x1+ 5x2 ≤ 30 x2 ≥ 0 x1 ≥ 0 and integers.
Use the linear finite difference algorithm to approximate the solution to the following problems.
Solve the following system of equations using the Gaussian algorithm with column pivoting and backward insertion: 2x2 − 4x3 + x4 = −8x1 + 2x2 + 3x3 − x4 = 3−3x1 + 2x3 + 2x4 = −32x1 + x2 − x4 = 2Column pivoting means that in the respective elimination stepsu. a row swap may be carried out in the respective elimination steps, so that the elimination elementa(m)mm is the largest element of the elimination column in terms of amount.
I need solution about exercise 6 but need Hint. Consider the Laurent decomposition at each Z k, and use Exercise 5.
Find z1 and z2. use gauss elimination, not gauss jordan
Solve the following system of equations using the Gaussian algorithm with column pivoting and backward insertion: 2x2 - 4x3 + x4 = -8x1 + 2x2 + 3x3 - x4 = 3-3x1 + 2x3 + 2x4 = -32x1 + x2 - x4 = 2 Here, column pivoting means that in the respective elimination stepsu. a row swap may be carried out in the respective elimination steps, so that the elimination elementa(m)mm is the largest element of the elimination column in terms of amount.
Given the following LP Max 4x1 + 6x2 s.t 1. 2x1 + 2x2 >_ 3, 2. x1 + 3x2 _> 2, 3. x1 + 3x2 _> 0, Find its dual LP. Use the graphical method or the Simplex algorithm, solve the primal LP in (1). Part 3. Use graphical method or the Simplex algorithm, solve the dual LP that you find in Part A Given the following LP Max 3x1 + 2x2 s.t 2x1 + x2 <_ 4, x1 + 3x2 <_ 6, x1 + x2 _< 0, Find its dual LP
Let A = 3 -7 -2 -3 5 1 6 -4 0 Use algorithm (Algorithm for an LU FactorizationReduce A to an echelon form U by a sequence of row operations, if possible. Place entries in L such that the same sequence of row operations reduces L to I) to find the lower and upper triangular matrix such that A=LU.
Draw a diagram to illustrate the divergence of the Gauss-Seidel method in a - 2b = 3 ,3a + 2b = 1
a) Discuss the Gramschmidth orthonormalization |Algorithm and relate it to a physical problem