Explanation Given: Minimum w = 15 y 1 + 12 y 2 Subject to y 1 + 2 y 2 ≤ 12 3 y 1 + y 2 ≥ 18 y 1 + y 2 = 10 and y 1 ≥ 0 , y 2 ≥ 0 . Calculation: To write the constraints as equations, add a slack variable for less than equal to ( ≤ ) term and subtract a surplus variable from more than equal to ( ≥ ) term. The minimization problem is solved by converting the objective function into maximization problem. Now, multiply on both sides of the objective function by − 1 . Maximize z = − w = − 15 y 1 − 12 y 2 The constraintcan be written as the following pair of inequalities, y 1 + y 2 ≤ 10 y 1 + y 2 ≥ 10 As y 1 + y 2 = 10 means when y 1 + y 2 ≤ 10 and simultaneously y 1 + y 2 ≥ 10 . Subject to y 1 + 2 y 2 + s 1 = 12 3 y 1 + y 2 − s 2 = 18 y 1 + y 2 + s 3 = 10 y 1 + y 2 − s 4 = 10 and y 1 ≥ 0 , y 2 ≥ 0 , s 1 ≥ 0 , s 2 ≥ 0 , s 3 ≥ 0 , s 4 ≥ 0 . And use the coefficient of above equations to write the initial simplex tableau while omitting the z column. Now the equations and the objective function can be written as following augmented matrix, and this the initial simplex table. y 1 y 2 s 1 s 2 s 3 s 4 [ 1 2 1 0 0 0 12 3 1 0 − 1 0 0 18 1 1 0 0 1 0 10 1 1 0 0 0 − 1 10 15 12 0 0 0 0 0 ] The variable whose columns have one entry that is ± 1 and the rest are 0 termed as basic variables and others as non-basic. So, From above table, the basic solution is: y 1 = 0 , y 2 = 0 , s 1 = 12 , s 2 = − 18 , s 3 = 10 , and s 4 = − 10 . However, because two variables are negative, the solution is not feasible. Now find the basic feasible solution. In basic solution given by tableau, s 2 and s 4 have negative value. The only non-zero entry in its column is the − 1 in row 1. Choose any positive entry in row 2 except the entry in the far right. The column that the chosen entry is in will be the pivot column. Here, the first column is the pivot column and the pivot row are considered by the smallest quotient. 12 1 = 12 , 18 3 = 6 , 10 1 = 10 , and 10 1 = 10 . The smallest quotient is 6 so the pivot is 3 in row 2 of column 1. Multiply by 1 3 to row 2 in order to make pivot element to 1 for easier calculations. y 1 y 2 s 1 s 2 s 3 s 4 [ 1 2 1 0 0 0 12 1 1 3 0 − 1 3 0 0 6 1 1 0 0 1 0 10 1 1 0 0 0 − 1 10 15 12 0 0 0 0 0 ] Then pivoting in the usual way leads to the tableau, by using operations R 1 − R 2 , R 3 − R 2 , R 4 − R 2 and R 5 − 15 R 2 to convert all elements of that column to zero except pivot element. y 1 y 2 s 1 s 2 s 3 s 4 [ 0 5 3 1 1 3 0 0 6 1 1 3 0 − 1 3 0 0 6 0 2 3 0 1 3 1 0 4 0 2 3 0 1 3 0 − 1 4 0 7 0 5 0 0 − 90 ] Still, it is not the basic feasible solution as s 4 is negative

Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)

11th Edition

ISBN: 9780321931078

Author: Margaret L. Lial, Thomas W. Hungerford, John P. Holcomb, Bernadette Mullins

Publisher: PEARSON

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Chapter 7.7, Problem 20E

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Chapter 7.7, Problem 19E

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Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)

Ch. 7.1 - Checkpoint 1 Graph the given...Ch. 7.1 - Prob. 2CP Ch. 7.1 - Prob. 3CP Ch. 7.1 - Prob. 4CP Ch. 7.1 - Prob. 5CP Ch. 7.1 - Checkpoint 6 Graph the feasible region of the...Ch. 7.1 - Prob. 7CP Ch. 7.1 - Match the inequality with its graph, which is one...Ch. 7.1 - Match the inequality with its graph, which is one...Ch. 7.1 - Match the inequality with its graph, which is one...

Ch. 7.1 - Prob. 4E Ch. 7.1 - Match the inequality with its graph, which is one...Ch. 7.1 - Match the inequality with its graph, which is one...Ch. 7.1 - Graph each of the given linear inequalities. (See...Ch. 7.1 - Graph each of the given linear inequalities. (See...Ch. 7.1 - Prob. 9E Ch. 7.1 - Graph each of the given linear inequalities. (See...Ch. 7.1 - Prob. 11E Ch. 7.1 - Graph each of the given linear inequalities. (See...Ch. 7.1 - Graph each of the given linear inequalities. (See...Ch. 7.1 - Graph each of the given linear inequalities. (See...Ch. 7.1 - Graph each of the given linear inequalities. (See...Ch. 7.1 - Graph each of the given linear inequalities. (See...Ch. 7.1 - Prob. 17E Ch. 7.1 - Graph each of the given linear inequalities. (See...Ch. 7.1 - Prob. 19E Ch. 7.1 - Graph each of the given linear inequalities. (See...Ch. 7.1 - Graph each of the given linear inequalities. (See...Ch. 7.1 - Prob. 22E Ch. 7.1 - Prob. 23E Ch. 7.1 - Graph each of the given linear inequalities. (See...Ch. 7.1 - Prob. 25E Ch. 7.1 - Prob. 26E Ch. 7.1 - Prob. 27E Ch. 7.1 - Prob. 28E Ch. 7.1 - Graph the feasible region for the given systems of...Ch. 7.1 - Graph the feasible region for the given systems of...Ch. 7.1 - Graph the feasible region for the given systems of...Ch. 7.1 - Prob. 32E Ch. 7.1 - Graph the feasible region for the given systems of...Ch. 7.1 - Prob. 34E Ch. 7.1 - Graph the feasible region for the given systems of...Ch. 7.1 - Graph the feasible region for the given systems of...Ch. 7.1 - Prob. 37E Ch. 7.1 - Prob. 38E Ch. 7.1 - Graph the feasible region for the given systems of...Ch. 7.1 - Prob. 40E Ch. 7.1 - Graph the feasible region for the given systems of...Ch. 7.1 - Graph the feasible region for the given systems of...Ch. 7.1 - Prob. 43E Ch. 7.1 - Graph the feasible region for the given systems of...Ch. 7.1 - Graph the feasible region for the given systems of...Ch. 7.1 - Graph the feasible region for the given systems of...Ch. 7.1 - Prob. 47E Ch. 7.1 - Prob. 48E Ch. 7.1 - Prob. 49E Ch. 7.1 - Prob. 50E Ch. 7.1 - Prob. 51E Ch. 7.1 - 52. Business A manufacturer of electric shavers...Ch. 7.1 - Prob. 53E Ch. 7.1 - Prob. 54E Ch. 7.1 - Prob. 55E Ch. 7.1 - Prob. 56E Ch. 7.2 - Checkpoint 1 Suppose the objective function in...Ch. 7.2 - Prob. 2CP Ch. 7.2 - Prob. 3CP Ch. 7.2 - Checkpoint 4 Use the region of feasible solutions...Ch. 7.2 - Prob. 5CP Ch. 7.2 - Prob. 6CP Ch. 7.2 - Exercises 1–6 show regions of feasible solutions....Ch. 7.2 - Exercises 1–6 show regions of feasible solutions....Ch. 7.2 - Exercises 1–6 show regions of feasible solutions....Ch. 7.2 - Exercises 1–6 show regions of feasible solutions....Ch. 7.2 - Exercises 1–6 show regions of feasible solutions....Ch. 7.2 - Prob. 6E Ch. 7.2 - Use graphical methods to solve Exercises 7–12....Ch. 7.2 - Use graphical methods to solve Exercises 7–12....Ch. 7.2 - Prob. 9E Ch. 7.2 - Use graphical methods to solve Exercises 7–12....Ch. 7.2 - Use graphical methods to solve Exercises 7–12....Ch. 7.2 - Use graphical methods to solve Exercises 7–12....Ch. 7.2 - Find the minimum and maximum values of (if...Ch. 7.2 - Find the minimum and maximum values of (if...Ch. 7.2 - Find the minimum and maximum values of (if...Ch. 7.2 - Find the minimum and maximum values of (if...Ch. 7.2 - Prob. 17E Ch. 7.2 - 18. Find values and that maximize subject to...Ch. 7.2 - Prob. 19E Ch. 7.2 - Prob. 20E Ch. 7.3 - Prob. 1CP Ch. 7.3 - Prob. 2CP Ch. 7.3 - Prob. 3CP Ch. 7.3 - Prob. 1E Ch. 7.3 - Prob. 2E Ch. 7.3 - Prob. 3E Ch. 7.3 - Write the constraints in Exercises 1–4 as linear...Ch. 7.3 - Prob. 5E Ch. 7.3 - Solve these linear programming problems, which are...Ch. 7.3 - Prob. 7E Ch. 7.3 - Solve these linear programming problems, which are...Ch. 7.3 - Prob. 9E Ch. 7.3 - Prob. 10E Ch. 7.3 - Prob. 11E Ch. 7.3 - Solve these linear programming problems, which are...Ch. 7.3 - Prob. 13E Ch. 7.3 - Solve the following linear programming problems....Ch. 7.3 - Prob. 15E Ch. 7.3 - Prob. 16E Ch. 7.3 - Prob. 17E Ch. 7.3 - Prob. 18E Ch. 7.3 - Prob. 19E Ch. 7.3 - Prob. 20E Ch. 7.3 - Prob. 21E Ch. 7.3 - Solve the following linear programming problems....Ch. 7.3 - Prob. 23E Ch. 7.3 - Prob. 24E Ch. 7.3 - Prob. 25E Ch. 7.3 - Prob. 26E Ch. 7.3 - Prob. 27E Ch. 7.3 - Prob. 28E Ch. 7.3 - Prob. 29E Ch. 7.4 - Prob. 1CP Ch. 7.4 - Prob. 2CP Ch. 7.4 - Prob. 3CP Ch. 7.4 - Prob. 4CP Ch. 7.4 - Prob. 5CP Ch. 7.4 - Prob. 6CP Ch. 7.4 - Prob. 1E Ch. 7.4 - Prob. 2E Ch. 7.4 - In Exercises 1–4, (a) determine the number of...Ch. 7.4 - Prob. 4E Ch. 7.4 - Prob. 5E Ch. 7.4 - Prob. 6E Ch. 7.4 - Prob. 7E Ch. 7.4 - Prob. 8E Ch. 7.4 - Prob. 9E Ch. 7.4 - Prob. 10E Ch. 7.4 - Prob. 11E Ch. 7.4 - Prob. 12E Ch. 7.4 - Prob. 13E Ch. 7.4 - Prob. 14E Ch. 7.4 - Prob. 15E Ch. 7.4 - Prob. 16E Ch. 7.4 - Prob. 17E Ch. 7.4 - Prob. 18E Ch. 7.4 - Prob. 19E Ch. 7.4 - Prob. 20E Ch. 7.4 - Prob. 21E Ch. 7.4 - Use the simplex method to solve Exercises...Ch. 7.4 - Prob. 23E Ch. 7.4 - Prob. 24E Ch. 7.4 - Prob. 25E Ch. 7.4 - Prob. 26E Ch. 7.4 - Prob. 27E Ch. 7.4 - Prob. 28E Ch. 7.4 - Prob. 29E Ch. 7.4 - Prob. 30E Ch. 7.4 - Prob. 31E Ch. 7.4 - Prob. 32E Ch. 7.4 - Use the simplex method to solve Exercises...Ch. 7.4 - Prob. 34E Ch. 7.4 - Use the simplex method to solve Exercises...Ch. 7.4 - Use the simplex method to solve Exercises...Ch. 7.4 - Prob. 37E Ch. 7.4 - Prob. 38E Ch. 7.5 - Prob. 1CP Ch. 7.5 - Prob. 1E Ch. 7.5 - Prob. 2E Ch. 7.5 - Prob. 3E Ch. 7.5 - Set up the initial simplex tableau for each of the...Ch. 7.5 - In each of the given exercises, (a) use the...Ch. 7.5 - In each of the given exercises, (a) use the...Ch. 7.5 - In each of the given exercises, (a) use the...Ch. 7.5 - Prob. 8E Ch. 7.5 - Prob. 9E Ch. 7.5 - Prob. 10E Ch. 7.5 - Prob. 11E Ch. 7.5 - Prob. 12E Ch. 7.5 - Prob. 13E Ch. 7.5 - Prob. 14E Ch. 7.5 - Prob. 15E Ch. 7.5 - Prob. 16E Ch. 7.5 - Prob. 17E Ch. 7.5 - Prob. 18E Ch. 7.5 - Prob. 19E Ch. 7.5 - Prob. 20E Ch. 7.5 - Prob. 21E Ch. 7.5 - Prob. 22E Ch. 7.6 - Checkpoint 1 Give the transpose of each...Ch. 7.6 - Prob. 2CP Ch. 7.6 - Prob. 3CP Ch. 7.6 - Prob. 4CP Ch. 7.6 - Prob. 5CP Ch. 7.6 - Prob. 6CP Ch. 7.6 - Prob. 1E Ch. 7.6 - Prob. 2E Ch. 7.6 - Prob. 3E Ch. 7.6 - Prob. 4E Ch. 7.6 - Prob. 5E Ch. 7.6 - Prob. 6E Ch. 7.6 - Prob. 7E Ch. 7.6 - Prob. 8E Ch. 7.6 - Prob. 9E Ch. 7.6 - Prob. 10E Ch. 7.6 - Prob. 11E Ch. 7.6 - Prob. 12E Ch. 7.6 - Prob. 13E Ch. 7.6 - Prob. 14E Ch. 7.6 - Prob. 15E Ch. 7.6 - Prob. 16E Ch. 7.6 - Prob. 17E Ch. 7.6 - Prob. 18E Ch. 7.6 - Prob. 19E Ch. 7.6 - Prob. 20E Ch. 7.6 - Prob. 21E Ch. 7.6 - Prob. 22E Ch. 7.6 - Prob. 23E Ch. 7.6 - Prob. 24E Ch. 7.6 - Prob. 25E Ch. 7.6 - Prob. 26E Ch. 7.6 - Prob. 27E Ch. 7.6 - 28. Business An animal food must provide at least...Ch. 7.6 - Prob. 29E Ch. 7.6 - 30. Business Joan McKee has a part-time job...Ch. 7.6 - Prob. 31E Ch. 7.6 - Prob. 32E Ch. 7.6 - Prob. 33E Ch. 7.6 - Prob. 34E Ch. 7.7 - Prob. 1CP Ch. 7.7 - Prob. 2CP Ch. 7.7 - Prob. 3CP Ch. 7.7 - Prob. 4CP Ch. 7.7 - Prob. 5CP Ch. 7.7 - Prob. 1E Ch. 7.7 - Prob. 2E Ch. 7.7 - Prob. 3E Ch. 7.7 - Prob. 4E Ch. 7.7 - Prob. 5E Ch. 7.7 - Prob. 6E Ch. 7.7 - Prob. 7E Ch. 7.7 - Prob. 8E Ch. 7.7 - Prob. 9E Ch. 7.7 - Prob. 10E Ch. 7.7 - Prob. 11E Ch. 7.7 - Prob. 12E Ch. 7.7 - Prob. 13E Ch. 7.7 - Prob. 14E Ch. 7.7 - Prob. 15E Ch. 7.7 - Prob. 16E Ch. 7.7 - Prob. 17E Ch. 7.7 - Prob. 18E Ch. 7.7 - Prob. 19E Ch. 7.7 - Prob. 20E Ch. 7.7 - Prob. 21E Ch. 7.7 - Prob. 22E Ch. 7.7 - Prob. 23E Ch. 7.7 - Prob. 24E Ch. 7.7 - Prob. 25E Ch. 7.7 - Prob. 26E Ch. 7.7 - Prob. 27E Ch. 7.7 - Prob. 28E Ch. 7.7 - Prob. 29E Ch. 7.7 - Prob. 30E Ch. 7.7 - Prob. 31E Ch. 7.7 - Prob. 32E Ch. 7.7 - Prob. 33E Ch. 7.7 - Prob. 34E Ch. 7.7 - Prob. 35E Ch. 7.7 - Use the two-stage method to solve Exercises 33–40....Ch. 7.7 - Prob. 37E Ch. 7.7 - Prob. 38E Ch. 7.7 - Prob. 39E Ch. 7.7 - Prob. 40E Ch. 7.7 - Prob. 41E Ch. 7.7 - Prob. 42E Ch. 7.7 - Prob. 43E Ch. 7 - Prob. 1CE Ch. 7 - 2. Consider preparing a stir-fry using beef, oil,...Ch. 7 - Prob. EP Ch. 7 - Prob. 1RE Ch. 7 - Prob. 2RE Ch. 7 - Graph each of the given linear inequalities. 3. Ch. 7 - Prob. 4RE Ch. 7 - Prob. 5RE Ch. 7 - Prob. 6RE Ch. 7 - Prob. 7RE Ch. 7 - Prob. 8RE Ch. 7 - Prob. 9RE Ch. 7 - Prob. 10RE Ch. 7 - Prob. 11RE Ch. 7 - Prob. 12RE Ch. 7 - Prob. 13RE Ch. 7 - Use the graphical method to solve Exercises...Ch. 7 - Use the graphical method to solve Exercises...Ch. 7 - Prob. 16RE Ch. 7 - Prob. 17RE Ch. 7 - Prob. 18RE Ch. 7 - 19. Finance The BlackRock Equity Dividend Fund...Ch. 7 - Prob. 20RE Ch. 7 - Prob. 21RE Ch. 7 - Prob. 22RE Ch. 7 - Prob. 23RE Ch. 7 - Prob. 24RE Ch. 7 - Prob. 25RE Ch. 7 - Prob. 26RE Ch. 7 - Prob. 27RE Ch. 7 - Prob. 28RE Ch. 7 - Prob. 29RE Ch. 7 - Prob. 30RE Ch. 7 - Prob. 31RE Ch. 7 - Prob. 32RE Ch. 7 - Prob. 33RE Ch. 7 - Prob. 34RE Ch. 7 - Prob. 35RE Ch. 7 - Prob. 36RE Ch. 7 - 37. When is it necessary to use the simplex method...Ch. 7 - Prob. 38RE Ch. 7 - 39. What kind of problem can be solved with the...Ch. 7 - 40. In solving a linear programming problem, you...Ch. 7 - Prob. 41RE Ch. 7 - Prob. 42RE Ch. 7 - Prob. 43RE Ch. 7 - Prob. 44RE Ch. 7 - Prob. 45RE Ch. 7 - Use the method of duals to solve these...Ch. 7 - Prob. 47RE Ch. 7 - Prob. 48RE Ch. 7 - Prob. 49RE Ch. 7 - Prob. 50RE Ch. 7 - Prob. 51RE Ch. 7 - Prob. 52RE Ch. 7 - Use the two-stage method to solve these...Ch. 7 - Prob. 54RE Ch. 7 - Prob. 55RE Ch. 7 - Prob. 56RE Ch. 7 - Business Solve the following maximization...Ch. 7 - Prob. 58RE Ch. 7 - Business Solve the following maximization...Ch. 7 - Prob. 60RE Ch. 7 - Prob. 61RE Ch. 7 - Business Solve the following minimization...Ch. 7 - Business Solve these mixed-constraint...Ch. 7 - Business Solve these mixed-constraint...

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