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mathematics
college mathematics for business economics

Questions and Answers of College Mathematics For Business Economics

In Problems 63–72, discuss the validity of each statement. Venn diagrams may be helpful. If the statement is true, explain why. If not, give a counterexample. If A C B, then AnB = A.
In Problems 59–64, construct a truth table to verify the implication or equivalence. b= (b d) v d
A medical researcher classifies subjects according to male or female; smoker or nonsmoker; and underweight, average weight, or overweight. How many combined classifications are possible? (A) Solve
In Problems 59–64, construct a truth table to verify each equivalence. (bnd)d = (b
In how many ways can 4 people sit in a row of 6 chairs?
In Problems 59–64, construct a truth table to verify the implication or equivalence. (p ^¬q) = p→q
In Problems 63–72, discuss the validity of each statement. Venn diagrams may be helpful. If the statement is true, explain why. If not, give a counterexample. If A C B, then AUB = A.
In how many ways can 3 people sit in a row of 7 chairs?
In Problems 59–64, construct a truth table to verify each equivalence. P→ (p^ q) = pq Р
In Problems 63–72, discuss the validity of each statement. Venn diagrams may be helpful. If the statement is true, explain why. If not, give a counterexample. If A UBA, then A C B.
A basketball team has 5 distinct positions. Out of 8 players, how many starting teams are possible if (A) The distinct positions are taken into consideration? (B) The distinct positions are not
Can a selection of r objects from a set of n distinct objects, where n is a positive integer, be a combination and a permutation simultaneously? Explain.
In Problems 63–72, discuss the validity of each statement. Venn diagrams may be helpful. If the statement is true, explain why. If not, give a counterexample. If An B = A, then A C B.
In Problems 63–72, discuss the validity of each statement. Venn diagrams may be helpful. If the statement is true, explain why. If not, give a counterexample. If AnB = Ø, then A= Ø.
A distribution center A wishes to send its products to five different retail stores: B, C, D, E, and F. How many different route plans can be constructed so that a single truck, starting from A, will
In Problems 63–72, discuss the validity of each statement. Venn diagrams may be helpful. If the statement is true, explain why. If not, give a counterexample. If A = Ø, then AnB = Ø.
Find the largest integer k such that your calculator can compute k! without an overflow error.
In Problems 63–72, discuss the validity of each statement. Venn diagrams may be helpful. If the statement is true, explain why. If not, give a counterexample. If A C B, then A' C B'.
Find the largest integer k such that your calculator can compute 2kCk without an overflow error.
In Problems 63–72, discuss the validity of each statement. Venn diagrams may be helpful. If the statement is true, explain why. If not, give a counterexample. If A C B, then B' CA'.
In a study of elderly couples, a sample of 8 couples aged 60 or more will be selected for medical tests from a group of 41 couples aged 60 or more. In how many ways can this be done?
In Problems 63–72, discuss the validity of each statement. Venn diagrams may be helpful. If the statement is true, explain why. If not, give a counterexample.The empty set is an element of every
An office supply store receives a shipment of 24 high-speed printers, including 5 that are defective. Three of these printers are selected for a store display. (A) How many selections can be
How many subsets does each of the following sets contain? (A) {a} (B) {a,b} (C) (a, b,c} (D) {a, b, c, d}
In Problems 63–72, discuss the validity of each statement. Venn diagrams may be helpful. If the statement is true, explain why. If not, give a counterexample.The empty set is a subset of the empty
Suppose that 6 female and 5 male applicants have been successfully screened for 5 positions. In how many ways can the following compositions be selected? (A) 3 females and 2 males (B) 4 females and
In Problems 91–98, use the Venn diagram to indicate which of the eight blood types are included in each set. An Rh
The company’s leaders in Problem 89 decide for or against certain measures as follows: The president has 2 votes and each vice-president has 1 vote. Three favorable votes are needed to pass a
In Problems 91–98, use the Venn diagram to indicate which of the eight blood types are included in each set. ANB
In Problems 91–98, use the Venn diagram to indicate which of the eight blood types are included in each set. AU Rh
In Problems 91–98, use the Venn diagram to indicate which of the eight blood types are included in each set. AUB
In Problems 91–98, use the Venn diagram to indicate which of the eight blood types are included in each set. (AUB)'
In Problems 91–98, use the Venn diagram to indicate which of the eight blood types are included in each set. (AUBURh)'
In Problems 91–98, use the Venn diagram to indicate which of the eight blood types are included in each set. Α΄ ΠΒ
In Problems 91–98, use the Venn diagram to indicate which of the eight blood types are included in each set. Rh'n A
Problems 5–8 refer to the system Find the solution of the system for which x2 = 0, s2 = 0. 2x₁ + 5x₂ + $1 x₁ + 3x₂ 10 + S₂ = 8
In Problems 1–8,(A) Introduce slack, surplus, and artificial variables and form the modified problem.(B) Write the preliminary simplex tableau for the modified problem and find the initial
In Problems 1–8, find the transpose of each matrix. 1 0 8 4 2 2 0 -1 - 1 -7 1 3
Form the dual problem of Minimize subject to C = 5x₁ + 3x2 3x₁ + 2x2 10 = 3x₁ + x₂ 20 0 X1, X₂ = X2
Problems 5–8 refer to the system Find the solution of the system for which x2 = 0, s1 = 0. 2x₁ + 5x₂ + $1 x₁ + 3x₂ 10 + S₂ = 8
In Problems 1–8,(A) Introduce slack, surplus, and artificial variables and form the modified problem.(B) Write the preliminary simplex tableau for the modified problem and find the initial
In Problems 1–8, find the transpose of each matrix. 1 1 4 -3 32 -1 -4 -5 87 3 90 0 6 0 -3 2 2 1 -1 1
Use the big M method to solve Problems 9–22. Minimize and maximize subject to 3x₁ + x₂ = 28 x2 x₁ + 2x₂ = 16 P = -4x₁ + 16x₂ X1, X₂ = 0 X2
Use the big M method to solve Problems 9–22. Minimize and maximize P = 2x₁ - x₂ subject to X₁ + x₂ = 8 5x₁ + 3x₂ = 30 X1, X2 = 0
Use the big M method to solve Problems 9–22. Maximize P = 2x₁ + 5x₂ subject to x₁ + 2x₂ = 18 2x₁ + x₂ = 21 IV IV x₁ + x₂ = 10 X1, X2 0
Use the big M method to solve Problems 9–22. Maximize subject to P = 6x₁ + 2x₂ x₁ + 2x₂ = 20 2x₁ + x₂ ≤ 16 x₁ + x₂ = 9 X1, X₂0 IV IV
Solve the linear programming problem using the simplex method. Maximize subject to P = 6x₁ + 8x₂ 6x₁ + 8x₂ = 48 6x₁ + 6x₂ = 42 8x14x2 40 X1, X2 = 0
Use the big M method to solve Problems 9–22. Maximize subject to 3x₁ + x₂ + 2x3 = 12 x₁ - x₂ + 2x3 = 6 х1, х2, х3 0 P = 10x₁ + 12x₂ + 20x3
Form the dual problem of the linear programming problem Minimize C = 2x₁ + 5x₂ subject to x₁ + 2x₂ = 10 3x₁ + x₂ 18 ≥ 4 X1, X₂0 X2 X₂
Use the big M method to solve Problems 9–22. Maximize subject to P = 5x₁ + 7x₂ + 9x3 X₁Xx₂ + x3 = 20 - 2x₁ + x₂ + 5x3 = 35 X1, X2, X3 = 0
Solve Problem 14 by applying the simplex method to the dual problem. Data in Problem 14Form the dual problem of the linear programming problem Minimize C = 2x₁ + 5x₂ subject to x₁ + 2x₂ =
Solve the linear programming problems in Problems 13–28 using the simplex method. Maximize subject to P = 2x₁ + 3x₂ -2x₁ + x₂ ≤ 2 -x₁ + x₂ = 5 X2 ≤ 6 X1, X₂0
Use the big M method to solve Problems 9–22. Minimize C = -5x₁12x₂ + 16x3 subject to x₁ + 2x₂ + x3 = 10 2x₁ + 3x₂ + x3 = 6 X3 2x₁ + x₂x3 X1, X2, X3 = 1 : 0 IV II
Solve the linear programming Problems 16 and 17. Maximize subject to x₁ - - P = 2x₁ + 5x₂ - 2x3 2x₂x32 2x₂ 3x₁ + 3x₂ - 4x3 ≤ 8 X1, X2, X3 = 0 х1, х2,
Use the big M method to solve Problems 9–22. Maximize C=-3x₁ + 15x₂ - 4x3 subject to 2x₁ + x₂ + 3x3 = 24 X₁ + 2x₂ + x3 = 6 x₁3x₂ + x3 = 2 0 х1, х2, X3 IV
Solve the linear programming Problems 16 and 17. Maximize subject to P = 2x₁ +5x₂2x3 x₁ - 2x₂ X3 ≤2 3x13x2 - 4x3 ≤ 8 X1, X2, X30
Solve the linear programming problems in Problems 13–28 using the simplex method. Maximize subject to P = -x₁ + 2x₂ x₁ + x₂ = 2 -x₁ + 3x₂ 12 X₁ - 4x₂ = 4 X1, X₂ = 0
Problems 17–26 refer to the table below of the six basic solutions to the e-system.In basic solution (A), which variables are basic? (A) (B) (C) (D) (E) (F) 2x + 3xz + S 4.x + 3x2 1 0 0 0 12 9 6 50
Use the big M method to solve Problems 9–22. Maximize subject to P = 3x₁ + 5x₂ + 6x3 2x₁ + x₂ + 2x3 ≤ 8 2x₁ + x₂ - 2x3 = 0 X1, X2, X30
In Problems 18 and 19,(A) Introduce slack, surplus, and artificial variables and form the modified problem.(B) Write the preliminary simplex tableau for the modified problem and find the initial
Problems 17–26 refer to the table below of the six basic solutions to the e-system.In basic solution (B), which variables are nonbasic? (A) (B) (C) (D) (E) (F) 2x + 3xz + S 4.x +
Use the big M method to solve Problems 9–22. Maximize P = 3x₁ + 6x₂ + 2x3 subject to 2x₁ +2x₂ + 3x3 ≤ 12 2x₁2x₂ + x3 = 0 X1, X2, X30
In Problems 18 and 19,(A) Introduce slack, surplus, and artificial variables and form the modified problem.(B) Write the preliminary simplex tableau for the modified problem and find the initial
Problems 17–26 refer to the table below of the six basic solutions to the e-system.In basic solution (C), which variables are nonbasic? (A) (B) (C) (D) (E) (F) 2x + 3xz + S 4.x +
Use the big M method to solve Problems 9–22. Maximize subject to P = 2x₁ + 3x₂ + 4x3 x₁ + 2x₂ + x3 ≤ 25 2x₁ + x₂ + 2x3 ≤ 60 x₁ + 2x₂x3 = 10 X3 X1, X2, X3 0
Problems 17–26 refer to the table below of the six basic solutions to the e-system.In basic solution (D), which variables are basic? (A) (B) (C) (D) (E) (F) 2x + 3xz + S 4.x + 3x2 1 0 0 0 12 9 6 50
Use the big M method to solve Problems 9–22. Maximize P = 5x₁ + 2x₂ + 9x3 subject to 2x₁ + 4x₂ + x3 = 150 3x₁ + 3x₂ + x3 ≤ 90 -X₁ + 5x₂ + x3 ≥ 120 X1, X₂, X3 = 0
Problems 17–26 refer to the table below of the six basic solutions to the e-system.In basic solution (E), which variables are nonbasic? (A) (B) (C) (D) (E) (F) 2x + 3xz + S 4.x +
Write a brief verbal description of the type of linear programming problem that can be solved by the method indicated in Problems 21–23. Include the type of optimization, the number of variables,
Use the big M method to solve Problems 9–22. Maximize subject to P = x₁ + 2x₂ + 5x3 x1 x₁ + 3x₂ + 2x3 ≤ 60 2x₁ + 5x₂ + 2x3 = 50 x₁2x₂ + x3 ≥ 40 X1, X2, X3 0
Problems 17–26 refer to the table below of the six basic solutions to the e-system.In basic solution (F), which variables are basic? (A) (B) (C) (D) (E) (F) 2x + 3xz + S 4.x + 3x2 1 0 0 0 12 9 6 50
Use the big M method to solve Problems 9–22. Maximize P = 2x₁ + 4x₂ + x3 subject to 2x₁ + 3x₂ +5x3 = 280 2x₁ + 2x₂ + x3 ≥ 140 2x₁ + x₂ ≥ 150 0 х1, х2, X3 IV
Problems 17–26 refer to the table below of the six basic solutions to the e-system.Which of the six basic solutions are feasible? Explain. (A) (B) (C) (D) (E) (F) 2x + 3xz + S 4.x +
Solve the linear programming problems in Problems 21–32 by applying the simplex method to the dual problem. Minimize subject to C = 10x₁ + 4x₂ 2x₁ + x₂ = 6 x₁4x₂ = -24 −8x -8rp + 5x
Solve the following linear programming problem by the simplex method, keeping track of the obvious basic solution at each step. Then graph the feasible region and illustrate the path to the optimal
Solve the linear programming problems in Problems 13–28 using the simplex method. Maximize subject to P = 4x₁ + 2x₂ + 3x3 x₁ + x₂ + x3 ≤ 11 2x1 + 3x₂ + x3 ≤ 20 x₁ + 3x₂ + 2x3 =
Problems 17–26 refer to the table below of the six basic solutions to the e-system.Which of the basic solutions are not feasible? Explain. (A) (B) (C) (D) (E) (F) 2x + 3xz + S 4.x +
Problems 17–26 refer to the table below of the six basic solutions to the e-system.Use the basic feasible solutions to maximize P = 2x1 + 5x2. (A) (B) (C) (D) (E) (F) 2x + 3xz + S 4.x +
Solve the linear programming problems in Problems 13–28 using the simplex method. Maximize subject to P=20x₁+30x₂ 0.6x₁ + 1.2x₂ ≤ 960 0.03x₁ +0.04x2 = 36 0.3x₁ + 0.2x2 ≤ 270 = 0 X1,
Problems 17–26 refer to the table below of the six basic solutions to the e-system.Use the basic feasible solutions to maximize P = 8x1 + 5x2. (A) (B) (C) (D) (E) (F) 2x + 3xz + S 4.x +
Solve by the dual problem method: Minimize C = 15x₁ + 12x₂ + 15x3 + 18x4 subject to x₁ + x₂ = 240 500 X3 + x4 x₁ + x3 = 400 x₂ + x4 ≥ 300 0 X1, X2, X3, X4
Solve the linear programming problems in Problems 13–28 using the simplex method. Maximize P = x₁ + 2x₂ + 3x3 subject to 2x₁ + 2x₂ + 8x3 = 600 x₁ + 3x₂ + 2x3 ≤ 600 3x₁ + 2x₂ + x3
Problems 27–36 refer to the partially completed table below of the 10 basic solutions to the e-systemIn basic solution (C), which variables are basic? x₁ + x₂ + $₁ 2x₁ + x₂ 4x₁ +
Solve the linear programming problems in Problems 13–28 using the simplex method. Maximize subject to P = 10x₁ + 50x₂ + 10x3 3x₁ + 3x₂ + 3x3 ≤ 66 48 6x₁2x₂ + 4x3 = 3x₁ + 6x₂ + 9x3
Problems 27–36 refer to the partially completed table below of the 10 basic solutions to the e-systemIn basic solution (E), which variables are nonbasic? x₁ + x₂ + $₁ 2x₁ + x₂ 4x₁ +
Problems 27–36 refer to the partially completed table below of the 10 basic solutions to the e-systemIn basic solution (G), which variables are nonbasic? x₁ + x₂ + $₁ 2x₁ + x₂ 4x₁ +
Problems 27–36 refer to the partially completed table below of the 10 basic solutions to the e-systemIn basic solution (I), which variables are basic? x₁ + x₂ + $₁ 2x₁ + x₂ 4x₁ +
Problems 27–36 refer to the partially completed table below of the 10 basic solutions to the e-systemWhich of the basic solutions (A) through (F) are not feasible? Explain. X₁ + x₂ + $₁ 2x₁
In Problems 29 and 30, first solve the linear programming problem by the simplex method, keeping track of the basic feasible solutions at each step. Then graph the feasible region and illustrate the
Solve Problems 31 and 32 by the simplex method and also by graphing (the geometric method). Compare and contrast the results. Maximize subject to P = 2x₁ + 3x₂ 2x₁ + x₂ ≤ 4 X₂10 : 0 X1, X2
Problems 27–36 refer to the partially completed table below of the 10 basic solutions to the e-systemWhich of the basic solutions (A) through (F) are feasible? Explain. x₁ + x₂ + $₁ 2x₁ +
Solve Problems 31 and 32 by the simplex method and also by graphing (the geometric method). Compare and contrast the results. Maximize subject to P = 2x₁ + 3x₂ x₁ + x₂ ≤ 2 x₂=4 X1, X₂ =
Problems 27–36 refer to the partially completed table below of the 10 basic solutions to the e-systemFind basic solution (G). x₁ + x₂ + $₁ 2x₁ + x₂ 4x₁ + x₂ +$2 = 24 = 30 + S3 = 48
In Problems 33–36, there is a tie for the choice of the first pivot column. Use the simplex method to solve each problem two different ways: first by choosing column 1 as the first pivot column,
Problems 27–36 refer to the partially completed table below of the 10 basic solutions to the e-systemFind basic solution (H). x₁ + x₂ + $₁ 2x₁ + x₂ 4x₁ + x₂ +$2 = 24 = 30 + S3 = 48
In Problems 33–36, there is a tie for the choice of the first pivot column. Use the simplex method to solve each problem two different ways: first by choosing column 1 as the first pivot column,
Problems 27–36 refer to the partially completed table below of the 10 basic solutions to the e-systemFind basic solution (I). x₁ + x₂ + $₁ 2x₁ + x₂ 4x₁ + x₂ +$2 = 24 = 30 + S3 = 48
A person on a high-protein, lowcarbohydrate diet requires at least 100 units of protein and at most 24 units of carbohydrates daily. The diet will consist entirely of three special liquid diet foods:
In Problems 33–36, there is a tie for the choice of the first pivot column. Use the simplex method to solve each problem two different ways: first by choosing column 1 as the first pivot column,
Problems 27–36 refer to the partially completed table below of the 10 basic solutions to the e-systemFind basic solution (J). x₁ + x₂ + $₁ 2x₁ + x₂ 4x₁ + x₂ +$2 = 24 = 30 + S3 = 48

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