Explanation Given Information: The provided constraints are x + 2 y ≥ 20 2 x + y ≥ 20 x ≥ 0 , y ≥ 0 Formula used: To convert the minimization problem to the maximization problem, multiply the objective function by − 1 . To compute solution of general linear programming problems, use slack and surplus variables to covert inequalities into equations and star the rows for which the active variables have negative value. If there are starred rows, use Phase I to proceed. Phase I: To remove the stars that is to make active variables have positive values. Start from the first starred row and locate the largest positive number and pivot the column, use test ratios and the smallest test ratio corresponds to a pivot and clear the pivot column. Check again and star the rows for which the active variables have negative value and repeat the process until there are no starred rows and move to Phase II. Phase II: Use the simplex method to solve the obtained standard maximization tableau. Choose the smallest negative number on the left side of the bottom row and pivot the column. 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. Clear the pivot column using the pivot and label the pivot row with the label of the pivot column. Repeat till all the entries in the bottom row are non negative. If there are no negative entries in the bottom row of the standard maximization tableau, then the obtained tableau represents the solution to the problem. Use row operations to clear the column of the augmented matrix. Calculation: Consider the objective function c = 6 x + 6 y of the minimization problem. Recall that to convert the minimization problem to the maximization problem, multiply the objective function by − 1 . − c = − ( 6 x + 6 y ) p = − 6 x − 6 y Thus, the corresponding maximization problem is Maximize p = − 6 x − 6 y subject to x + 2 y ≥ 20 2 x + y ≥ 20 x ≥ 0 , y ≥ 0 Consider the constraints x + 2 y ≥ 20 2 x + y ≥ 20 x ≥ 0 , y ≥ 0 Recall that to compute solution of general linear programming problems, use slack and surplus variables to covert inequalities into equations and star the rows for which the active variables have negative value. Subtract the surplus variable s and t . x + 2 y − s = 20 2 x + y − t = 20 Thus, the equations are x + 2 y − s = 20 2 x + y − t = 20 6 x + 6 y + p = 0 Write the equations in augmented matrix. x y s t p s 1 2 − 1 0 0 20 t 2 1 0 − 1 0 20 p 6 6 0 0 1 0 Check the values of the active variables s , t . s = 20 − 1 = − 20 t = 20 − 1 = − 20 Since, the value of s and t is negative, star the s and t row. Thus, the tableau is x y s t p * s 1 2 − 1 0 0 20 * t 2 1 0 − 1 0 20 p 6 6 0 0 1 0 Since, there are starred rows, use Phase I to proceed. Phase I: To remove the stars that is to make active variables have positive values. Start from the first starred row and locate the largest positive number and pivot the column, use test ratios and the smallest test ratio corresponds to a pivot and clear the pivot column. Check again and star the rows for which the active variables have negative value and repeat the process until there are no starred rows and move to Phase II. The first starred row is s and the largest positive number in the t row is 2. Thus, pivot the y column. The test ratios are 20 2 = 10 and 20 1 = 20 . Since, 10 is the smallest, pivot the entry 2 in y column. x y s t p * s 1 2 − 1 0 0 20 * t 2 1 0 − 1 0 20 p 6 6 0 0 1 0 Use row operations 2 R 2 − R 1 and R 3 − 3 R 1 to clear the pivot column of the augmented matrix

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 6.4, Problem 11E

To determine

To calculate: The minimum value of c=6x+6y subject to

x+2y≥202x+y≥20x≥0,y≥0

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.4, Problem 10E

Chapter 6.4, Problem 12E

Students have asked these similar questions

This question is a previous exam question. I am using it for practice but am stuck

in Q. A firm price of 501: If the Total cast is given by perfect competition sells its products at the TTC = 3Q² +2Q+5. level of output will will be the level of profit at What What Devive the Consumer Curve approach. demand the function maximize this firm's, that using putput level. the indifference prpfit. Q₂. The Total Cost equation in the production of bacon has hypothetical factor a 2 A C= "TC 1000+ 159" +03 ; Where ç. Kash, Bacao - metric bone Compute and 11" tonnes the and average cost at output level of 10. Stretch theme marginal cost of the the shope Carve an the production average, Cost arve 12 tonnes and explain, the relationship between Marginal Cost product es tamen op d Galaxy A71 01 Curve in

if w(x, y, z) = sin' ( xyz) (y zî + x z j + xy k) Find grad (div) at (0.5, 1, 0.5) (xyz)2

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 minimum value of c = 6 x + 6 y subject to x + 2 y ≥ 20 2 x + y ≥ 20 x ≥ 0 , y ≥ 0

Solution Summary: The author explains the simplex method to solve the obtained standard maximization tableau.

Videos

To calculate: The minimum value of c=6x+6y subject to

x+2y≥202x+y≥20x≥0,y≥0

Want to see the full answer?

Chapter 6 Solutions

The minimum value of c = 6 x + 6 y subject to x + 2 y ≥ 20 2 x + y ≥ 20 x ≥ 0 , y ≥ 0

Solution Summary: The author explains the simplex method to solve the obtained standard maximization tableau.

Videos

To calculate: The minimum value of c=6x+6y subject to x+2y≥202x+y≥20x≥0,y≥0

Want to see the full answer?

Chapter 6 Solutions

To calculate: The minimum value of c=6x+6y subject to

x+2y≥202x+y≥20x≥0,y≥0