Introduction to mathematical programming
Introduction to mathematical programming
4th Edition
ISBN: 9780534359645
Author: Jeffrey B. Goldberg
Publisher: Cengage Learning
Expert Solution & Answer
Book Icon
Chapter 2.1, Problem 2P

Explanation of Solution

Relating two vectors using matrix multiplication:

Suppose that at the beginning of each year, people change the beer they drink.

Let for i=1,2,3,....xi be the number of people who prefer beer “i” at the beginning of this month, and yi be the number of people who prefer beer “i” at the beginning of next month.

Since 30% of the people who prefer beer 1 switch to beer 2 and 20% of the people switch to beer 3, so the remaining 50% continue to be with beer 1. Also, 10% of people who prefer beer 3 switch to beer 1.

Hence, the number of people who prefer beer 1 in the beginning of next month is given below:

  y1=0.5x1+0.1x3

Now, 30% of the people who prefer beer 2 switch to beer 3 and the remaining 70% of the people continue to be with beer 2. Also, 30% of people who prefer beer 3 switch to beer 2 and 30% of the people who prefer beer 1 switch to beer 2.

Hence, the number of people who prefer beer 2 in the beginning of next month is given below:

  y2=0.3x1+0.7x2+0.3x3

Then, 30% of the people who prefer beer 3 switch to beer 2 and 10% of the people switch to beer 1, so the remaining 60% continue to be with beer 3. Also, 20% of people who prefer beer 1 switch to beer 3 and 30% of the people who prefer beer 2 switch to beer 3.

Hence, the number of people who prefer beer 3 in the beginning of next month is given below:

  y3=0.2x1+0

Blurred answer
Students have asked these similar questions
5. Suppose that a mass of 5 stretches a spring 10. The mass is acted on by an external force of F(t)=10 sin () and moves in a medium that gives a damping coefficient of ½. If the mass is set in motion with an initial velocity of 3 and is stretched initially to a length of 5. (I purposefully removed the units- don't worry about them. Assume no conversions are needed.) a) Find the equation for the displacement of the spring mass at time t. b) Write the equation for the displacement of the spring mass in phase-mode form. c) Characterize the damping of the spring mass system as overdamped, underdamped or critically damped. Explain how you know. D.E. for Spring Mass Systems k m* g = kLo y" +—y' + — —±y = —±F(t), y(0) = yo, y'(0) = vo m 2 A₁ = √c₁² + C₂² Q = tan-1
4. Given the following information determine the appropriate trial solution to find yp. Do not solve the differential equation. Do not find the constants. a) (D-4)2(D+ 2)y = 4e-2x b) (D+ 1)(D² + 10D +34)y = 2e-5x cos 3x
9.7 Given the equations 0.5x₁-x2=-9.5 1.02x₁ - 2x2 = -18.8 (a) Solve graphically. (b) Compute the determinant. (c) On the basis of (a) and (b), what would you expect regarding the system's condition? (d) Solve by the elimination of unknowns. (e) Solve again, but with a modified slightly to 0.52. Interpret your results.
Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Text book image
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Text book image
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Text book image
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Text book image
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Text book image
College Algebra
Algebra
ISBN:9781938168383
Author:Jay Abramson
Publisher:OpenStax