Explanation Given: The given problem is, Maximize P = 2 x + y + z subject to x + 2 y + 3 z ≤ 28 2 x + 3 y − z ≤ 6 x − 2 y + z ≥ 4 x ≥ 0 , y ≥ 0 , z ≥ 0 Approach: 1. In the standard maximization problem the objective function is to be maximized. 2. All variable involved in the problem should be non negative. 3. Each linear constraint may be written so that the expression involving the variables is less than or equal to a non negative constraint. 4. The optimal solution is reached when all the entries of bottom row of the simplex tableau are non negative. Calculation: Consider the given linear programming problem. Change all the constraints signs as ≤ . Maximize P = 2 x + y + z subject to x + 2 y + 3 z ≤ 28 2 x + 3 y − z ≤ 6 − x + 2 y − z ≤ − 4 x ≥ 0 , y ≥ 0 , z ≥ 0 Introduce the slack variables u v and w in the given linear programming problem, x + 2 y + 3 z + u = 28 2 x + 3 y − z + v = 6 − x + 2 y − z + w = − 4 − 2 x − y − z + P = 0 The initial simplex tableau is, x y z u v w P Constant 1 2 3 1 0 0 0 28 ( 2 ) 3 − 1 0 1 0 0 6 − 1 2 − 1 0 0 1 0 − 4 − 2 − 1 − 1 0 0 0 1 0 Table ( 1 ) At x = 0 , y = 0 , z = 0 we have u = 28 , v = 6 , w = − 4 , P = 0 In the initial simplex tableau the minimum value for bottom row is − 2 so pivot this column, The pivoted element is 2 and apply 1 2 R 2 . x y z u v w P Constant 1 2 3 1 0 0 0 28 ( 1 ) 3 2 − 1 2 0 1 2 0 0 3 − 1 2 − 1 0 0 1 0 − 4 − 2 − 1 − 1 0 0 0 1 0 Table ( 2 ) Now apply R 1 − R 2 , R 3 + R 2 and R 4 + 2 R 2

Bundle: Finite Mathematics For The Managerial, Life, And Social Sciences, 12th + Student Solutions Manual

12th Edition

ISBN: 9781337762182

Author: Soo T. Tan

Publisher: Cengage Learning

See similar textbooks

Videos

Question

Chapter 4.3, Problem 17E

To determine

To solve:

The given linear programming problem.

Maximize P=2x+y+z

subject to x+2y+3z≤28 2x+3y−z≤6 x−2y+z≥4 x≥0,y≥0,z≥0

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.3, Problem 16E

Chapter 4.3, Problem 18E

Students have asked these similar questions

At a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is 0.49. Find the probability that in a sample of 13 customers, at least 7 will order a nonalcoholic beverage

10. In the general single period market model with = {W1, W2, W3}, one risky asset, S, and a money market account, we have So = 4 for the risky asset. Moreover, the effective rate of interest on the money market account is 5% and at time t = 1 we have W1 W2 W3 S₁ 100 50 40 21 21 21 (a) Calculate all risk-neutral probability measures for this model. [4 Marks] (b) State if the model is arbitrage-free. Give a brief reason for your answer. [2 Marks] (c) A large bank has designed an investment product with payoff X at time t = 1. Given W₁ W2 W3 X 0 1 1.5 show that X is an attainable contingent claim. [4 marks]

Question 1. (10 points) A researcher is studying tumours in mice. The growth rate for the volume of the tumour V(t) in cm³ is given by dV = 1.45V(2 In(V+1)). dt (a) (4 pts) Find all the equilibria and determine their stability using the stability condition. (b) (2 pts) Draw the phase plot f(V) versus V where f(V) = V'. You may find it helpful to use Desmos or Wolfram Alpha to plot the graph of f(V) versus V (both are free to use online), or you can plot it by hand if you like. On the plot identify each equilibrium as stable or unstable. (c) (4 pts) Draw direction arrows for the case where the tumour starts at size 3cm³ and for the case where the tumour starts at size 9cm³. Explain in biological terms what happens to the size of each of these tumours at time progresses.

Chapter 4 Solutions

Bundle: Finite Mathematics For The Managerial, Life, And Social Sciences, 12th + Student Solutions Manual

Ch. 4.1 - Give the three characteristics of a standard...Ch. 4.1 - a. When the initial simplex tableau is set up, how...Ch. 4.1 - In the simplex method, how is a pivoted column...Ch. 4.1 - In Exercises 1-6, a write the linear programming...Ch. 4.1 - In Exercises 1-6, a write the linear programming...Ch. 4.1 - In Exercises 1-6, a write the linear programming...Ch. 4.1 - In Exercises 1-6, a write the linear programming...Ch. 4.1 - In Exercises 1-6, a write the linear programming...Ch. 4.1 - Prob. 6E Ch. 4.1 - In Exercises 7-16, determine whether the given...

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 given linear programming problem. Maximize P = 2 x + y + z subject to x + 2 y + 3 z ≤ 28 2 x + 3 y − z ≤ 6 x − 2 y + z ≥ 4 x ≥ 0 , y ≥ 0 , z ≥ 0

Solution Summary: The author explains that the optimal solution for linear programming problem is x=467,y=0,z=

Videos

To solve:

The given linear programming problem.

Maximize P=2x+y+z

subject to x+2y+3z≤28 2x+3y−z≤6 x−2y+z≥4 x≥0,y≥0,z≥0

Want to see the full answer?

Chapter 4 Solutions

The given linear programming problem. Maximize P = 2 x + y + z subject to x + 2 y + 3 z ≤ 28 2 x + 3 y − z ≤ 6 x − 2 y + z ≥ 4 x ≥ 0 , y ≥ 0 , z ≥ 0

Solution Summary: The author explains that the optimal solution for linear programming problem is x=467,y=0,z=

Videos

To solve: The given linear programming problem. Maximize P=2x+y+z subject to x+2y+3z≤28 2x+3y−z≤6 x−2y+z≥4 x≥0,y≥0,z≥0

Want to see the full answer?

Chapter 4 Solutions

To solve:

The given linear programming problem.

Maximize P=2x+y+z

subject to x+2y+3z≤28 2x+3y−z≤6 x−2y+z≥4 x≥0,y≥0,z≥0