Explanation Given Information: The provided matrix is: Maximize p = 2 x + y Subject to x + 2 y ≥ 12 , 2 x + y ≤ 12 , x + y ≤ 5 and x ≥ 0 , y ≥ 0 Formula used: Following steps of the simplex method, Step 1: Use slack variables and write the inequalities in equation form. Step 2: Write the equations in an augmented matrix. Step 3: Choose the smallest negative number on the left side of the bottom row and pivot the column. Step 4: Select the pivot which is the smallest of the test ratios a b , where a is the entry in the right most column and b is the corresponding entry in the pivot column. Step 5: Clear the pivot column using the pivot and label the pivot row with the label of the pivot column. Step 6: Repeat the above steps till all the entries in the bottom row are non-negative. Use row operations to clear the column of the augmented matrix. Calculation: Consider the provided matrix is: Maximize p = 2 x + y Subject to x + 2 y ≥ 12 , 2 x + y ≤ 12 , x + y ≤ 5 and x ≥ 0 , y ≥ 0 Step 1) Use slack variables and write the inequalities in equation form. x + 2 y − s = 12 2 x + y + t = 12 x + y + u = 5 − 2 x − y + p = 0 Step 2) Write the equations in an augmented matrix. x y s t u p s 1 2 − 1 0 0 0 12 t 2 1 0 1 0 0 12 u 1 1 0 0 1 0 5 p − 2 − 1 0 0 0 1 0 Step 3) Choose the smallest negative number on the left side of the bottom row and pivot the column. The most negative entry in the bottom row is the 1 in the x − column So use this column as the pivot column

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

See similar textbooks

Videos

Question

Chapter 6, Problem 12RE

To determine

To calculate: The linear programming problem using simplex method.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6, Problem 11RE

Chapter 6, Problem 13RE

Students have asked these similar questions

3.1 Limits 1. If lim f(x)=-6 and lim f(x)=5, then lim f(x). Explain your choice. x+3° x+3* x+3 (a) Is 5 (c) Does not exist (b) is 6 (d) is infinite

1 pts Let F and G be vector fields such that ▼ × F(0, 0, 0) = (0.76, -9.78, 3.29), G(0, 0, 0) = (−3.99, 6.15, 2.94), and G is irrotational. Then sin(5V (F × G)) at (0, 0, 0) is Question 1 -0.246 0.072 -0.934 0.478 -0.914 -0.855 0.710 0.262 .

2. Answer the following questions. (A) [50%] Given the vector field F(x, y, z) = (x²y, e", yz²), verify the differential identity Vx (VF) V(V •F) - V²F (B) [50%] Remark. You are confined to use the differential identities. Let u and v be scalar fields, and F be a vector field given by F = (Vu) x (Vv) (i) Show that F is solenoidal (or incompressible). (ii) Show that G = (uvv – vVu) is a vector potential for F.

Chapter 6 Solutions

Finite Mathematics and Applied Calculus (MindTap Course List)

Ch. 6.1 - In Exercises 1-26, sketch the region that...Ch. 6.1 - In Exercises 1-26, sketch the region that...Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - In Exercises 1-26, sketch the region that...Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E

Knowledge Booster

$Calculus$

Learn more about

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

The linear programming problem using simplex method.

Solution Summary: The author explains how to calculate the linear programming problem using simplex method.

Videos

To calculate: The linear programming problem using simplex method.

Want to see the full answer?

Chapter 6 Solutions