Explanation Method used: Solving a Nonstandard Problem: 1. If necessary, convert the problem to a maximization problem. (If the minimization problem has objective function w , rewrite as a maximization problem with the same constraints and objective function z = − w ). 2. Add slack variables and subtract surplus variables as needed. 3. Write the initial simplex tableau. 4. If any basic variable has a negative value, locate the nonzero number in that variable`s column, and note what row it is in. 5. In the row located in Step 4, find the positive entry that is farthest to the left, and note what column it is in. 6. In the column found in Step 5, choose a pivot by investigating quotients. 7. Use the row operations to change the other numbers in the pivot column to 0. 8. Continue Step 4through 7 until all basic variables are nonnegative. If it never becomes impossible to continue, then the problem has no feasible solution. 9. Once, a feasible solution has been found, continue to use the simplex method until the optimal solution is not found. Calculation: The linear programming problem is, Maximize : z = 6 x 1 + 2 x 2 subject t o : 2 x 1 + x 2 ≥ 20 2 x 1 + 5 x 2 ≤ 80 with x 1 ≥ 0 , x 2 ≥ 0. . Note that the above linear programming problem is maximization type. So it is in standard form. Subtract a surplus variable s 1 in first constraint and add a slack variable s 2 in second constraint and rewrite the linear programming problem as follows. Maximize : z = 6 x 1 + 2 x 2 subject t o : 2 x 1 + x 2 − s 1 = 20 2 x 1 + 5 x 2 + s 2 = 80 with x 1 ≥ 0 , x 2 ≥ 0 , s 1 ≥ 0 , s 2 ≥ 0. (1) The system (1) can be written in the system linear of equation as, 2 x 1 + x 2 − s 1 = 20 2 x 1 + 5 x 2 + s 2 = 80 − 6 x 1 − 2 x 2 + z = 0 Construct the initial simplex tableau form the above linear system as follows. [ x 1 x 2 s 1 s 2 z 2 1 − 1 0 0 20 2 5 0 1 0 80 − 6 − 2 0 0 1 0 ] Look the 2 × 2 identity matrix. So the basic variables are s 1 and s 2 . Thus, the basic solution is x 1 = 0 , x 2 = 0 , s 1 = − 20 , s 2 = 80 and z = 0

Finite Mathematics and Calculus with Applications (10th Edition)

10th Edition

ISBN: 9780321979407

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 4.4, Problem 10E

To determine

To find: The value of x1≥0 and x2≥0 using simplex method.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.4, Problem 9E

Chapter 4.4, Problem 11E

Students have asked these similar questions

A particle travels along a straight line path given by s=9.5t3-2.2t2-4.5t+9.9 (in meters). What time does it change direction? Report the higher of the answers to the nearest 2 decimal places in seconds.

Use the method of disks to find the volume of the solid that is obtained when the region under the curve y = over the interval [4,17] is rotated about the x-axis.

1. Find the area of the region enclosed between the curves y = x and y = x. Sketch the region.

Chapter 4 Solutions

Finite Mathematics and Calculus with Applications (10th Edition)

Ch. 4.1 - Prob. 1YT Ch. 4.1 - Prob. 2YT Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Convert each inequality into an equation by adding...Ch. 4.1 - For Exercises 58, (a) determine the number of...Ch. 4.1 - Prob. 6E Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E

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 value of x 1 ≥ 0 and x 2 ≥ 0 using simplex method.

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

Videos

To find: The value of x1≥0 and x2≥0 using simplex method.

Want to see the full answer?

Chapter 4 Solutions