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Questions and Answers of Mathematics Economics Business

In how many different ways can 6 candidates for an office be listed on a ballot?
Solve the following system of linear inequalities graphically and find the corner points: 5x + y = 20 x + y = 12 x + 3y = 18 x ≥ 0 y ≥ 0
(A) Maximize and minimize z = 4x + 2y subject to the constraints given in Example 2A.(B) Maximize and minimize z = 20x + 5y subject to the constraints given in Example 2B.
Refer to the following system of linear inequalities:Is the point (4, 5) in the solution region? 4x + y = 20 3x + 5y = 37 x ≥ 0 y ≥ 0
In Example 2B we saw that there was no optimal solution for the problem of maximizing the objective function z over the feasible region S. We want to add an additional constraint to modify the
Find M–1, given M = 4 -6 2
In Problem write the augmented matrix of the system of linear equations. X1 X₂ X2 X₁ + 3x₂ + 6x3 2 X3 = 5 = 7 ||
Solve by Gauss–Jordan elimination:2x1 – 4x2 – x3 = –84x1 – 8x2 + 3x3 = 4–2x1 + 4x2 + x3 = 11
In Problem solve each equation for x, where x represents a real number.4x = 8x + 7
Find M–1, given M = 2 1 -6 -2
Find: 1.3 10 0.2 3.5
In Problem solve each equation for x, where x represents a real number.x = 0.9x + 10
An investment advisor currently has two types of investments available for clients: a conservative investment A that pays 5% per year and a higher risk investment B that pays 10% per year. Clients
Solve by Gauss–Jordan elimination:3x1 + 6x2 – 9x3 = 152x1 + 4x2 – 6x3 = 10–2x1 – 3x2 + 4x3 = –6
Refer to the following matrices:What is the size of A? Of C? 2 -4 0 A=8 19 6 -5 B = D -19 0 8 7 2 4 0 C = [2 -3 0] || -4 ∞
Repeat Example 4 with investment A paying 4% and investment B paying 12%.Data from Example 4An investment advisor currently has two types of investments available for clients: a conservative
Solve by substitution:3x + 2y = –22x – y = –6
Find M–1, given M = 2 -3 -4 6
In Problem find the additive inverse and the multiplicative inverse, if defined, of each real number.(A) 4/5 (B) 12/7 (C) –2.5
Solve by Gauss–Jordan elimination:2x1 – 2x2 – 4x3 = –23x1 – 3x2 – 6x3 = –3–2x1 + 3x2 + x3 = 7
In Problem write the augmented matrix of the system of linear equations. 3x1 + 4x2 X₁ + 5x3 = 10 15 20 = - X2 + X3 =
In Problem solve each equation for x, where x represents a real number.6x = –3x + 14
Repeat Example 5 withData from Example 5Ms. Smith and Mr. Jones are salespeople in a new-car agency that sells only two models. August was the last month for this year’s models, and next year’s
In Problem solve each equation for x, where x represents a real number.x = 0.6x + 84
Find N–1, given N = [3 6 2
The message below was also encoded with the matrix A in Example 5. Decode this message:Data from Example 5The messagewas encoded with the matrix A shown next. Decode this message. 46 84 85 28 47 46 4
Refer to the following matrices:Which of the matrices is a column matrix? 2 -4 0 A=8 19 6 -5 B = D -19 0 8 7 2 4 0 C = [2 -3 0] || -4 ∞
The messagewas encoded with the matrix A shown next. Decode this message. 46 84 85 28 47 46 4 5 10 30 48 72 29 57 38 38 57 95
Solve by Gauss–Jordan elimination:x1 + 2x2 + 4x3 + x4 - x5 = 12x1 + 4x2 + 8x3 + 3x4 – 4x5 = 2x1 + 3x2 + 7x3 + 3x5 = –2
Solve the following system using elimination by addition:5x – 2y = 122x + 3y = 1
Refer to the following matrices:Which of the matrices is a row matrix? 2 -4 0 A=8 19 6 -5 B = D -19 0 8 7 2 4 0 C = [2 -3 0] || -4 ∞
Solve by Gauss–Jordan elimination:x1 – x2 + 2x3 – 2x5 = 3–2x1 + 2x2 - 4x3 – x4 + x5 = –53x1 – 3x2 + 7x3 + x4 – 4x5 = 6
In Problem solve each equation for x, where x represents a real number.6x + 8 = –2x + 17
A company that rents small moving trucks wants to purchase 25 trucks with a combined capacity of 28,000 cubic feet. Three different types of trucks are available: a 10-foot truck with a capacity of
A company that rents small moving trucks wants to purchase 16 trucks with a combined capacity of 19,200 cubic feet. Three different types of trucks are available: a cargo van with a capacity of 300
In Problem solve each equation for x, where x represents a real number.x = 0.2x + 3.2
Dennis wants to use cottage cheese and yogurt to increase the amount of protein and calcium in his daily diet. An ounce of cottage cheese contains 3 grams of protein and 15 milligrams of calcium. An
In Problem solve each equation for x, where x represents a real number.–4x + 3 = 5x + 12
If the factory in Example 7 also produces a trick water ski that requires 5 labor-hours in the assembly department and 1.5 labor-hours in the finishing department, write a product between appropriate
In Problem solve each equation for x, where x represents a real number.x = 0.3x + 4.2
Refer to the following matrices:Which of the matrices is a square matrix? 2 -4 0 A=8 19 6 -5 B = D -19 0 8 7 2 4 0 C = [2 −3 0] || -4 ∞
Find the equilibrium quantity and equilibrium price, and graph the following price–supply and price–demand equations: p=0.08q + 0.66 P = -0.1q + 3 Price-supply equation Price-demand equation
In Problem solve each equation for x, where x represents a real number.10 – 3x = 7x + 9
Find each product, if it is defined: (A) [ 0 3 [ 2 2 0 1 2 - -2 BRA [- -2 1 -2. [] 1] 2 (C) T 1 (E) [3 1 -2 42 M 2 3 1 0 (B) (D) 1 2 1 -2 3 0 4 -2 0 3 2 2 4 (F) 2 [3 2 1] 3 2 -2 -2 0]
Refer to the following matrices:Which of the matrices does not contain the element 0? 2 -4 0 A=8 19 6 -5 B = D -19 0 8 7 2 4 0 C = [2 −3 0] || -4 ∞
Refer to Example 10. The company wants to know how many hours to schedule in each department in order to produce 2,000 trick skis and 1,000 slalom skis. These production requirements can be
In Problem solve each equation for x, where x represents a real number.x = 0.68x + 2.56
In Problem solve each equation for x, where x represents a real number.2x + 7x + 1 = 8x + 3 – x
Find a, b, c, and d so that 6 0 -31][a b]-[-26 d 24 c 64 -6]
In Problem solve each equation for x, where x represents a real number.x = 0.98x + 8.24
Refer to the following matrices:List the elements on the principal diagonal of A 2 -4 0 A=8 19 6 -5 B = D -19 0 8 7 2 4 0 C = [2 -3 0] || -4 ∞
Refer to the following matrices:List the elements on the principal diagonal of B. 2 -4 0 A=8 19 6 -5 B = D -19 0 8 7 2 4 0 C = [2 -3 0] || -4 ∞
Refer to the following matrices:For matrix B, list the elements b31, b22, b13. 2 -4 0 A=8 19 6 -5 B = D -19 0 8 7 2 4 0 C = [2 −3 0] || -4 ∞
In which of Problems 20, 22, 24, 26, and 28 is the number of leftmost ones equal to the number of variables?Data from Problem 20Write the solution of the linear system corresponding to each reduced
Refer to the following matrices:For matrix A, list the elements a21, a12. 2 -4 0 A=8 19 6 -5 B = D -19 0 8 7 2 4 0 C = [2 −3 0] || -4 ∞
In which of Problems 19, 21, 23, 25, and 27 is the number of leftmost ones equal to the number of variables?Data from Problem 19Write the solution of the linear system corresponding to each reduced
Problem pertain to the following input–output model: Assume that an economy is based on three industrial sectors: agriculture (A), building (B), and energy (E). The technology matrix M and final
Refer to the following matrices:For matrix C, find c11 + c12 + c13. 2 -4 0 A=8 19 6 -5 B = D -19 0 8 7 2 4 0 C = [2 -3 0] || -4 ∞
Refer to the following matrices:For matrix D, find d11 + d21. 2 -4 0 A=8 19 6 -5 B = D -19 0 8 7 2 4 0 C = [2 -3 0] || -4 ∞
Solve the system in Problem 26A by writing the system as a matrix equation and using the inverse of the coefficient matrix (see Problem 25). Also, solve the system if the constants 1, 3, and 3 are
Solve by Gauss–Jordan elimination: 3 (A) x₁ + 2x₂ + 3x3 = 1 2x₁ + 3x₂ + 4x3 = 3 X₁ + 2x₂ + x3 = 3 X₁ + 2x₂x3 = -X3 2 2x₁3x₂ + x3 3x₁ + 5x₂ (C) x₁ + x₂ + x3 = X2 (B) =
Problem pertain to the following input–output model: Assume that an economy is based on three industrial sectors: agriculture (A), building (B), and energy (E). The technology matrix M and final
Problem pertain to the following input–output model: Assume that an economy is based on three industrial sectors: agriculture (A), building (B), and energy (E). The technology matrix M and final
The technology matrix for an economy based on energy (E) and mining (M) isThe management of these two sectors would like to set the total output level so that the final demand is always 40% of the
In which of Problems 20, 22, 24, 26, and 28 is the number of leftmost ones less than the number of variables?Data from Problem 20Write the solution of the linear system corresponding to each reduced
In Problems write each system as a matrix equation and solve using inverses.x1 + 2x2 = k1x1 + 3x2 = k2(A) k1 = 1, k2 = 3(B) k1 = 3, k2 = 5(C) k1 = –2, k2 = 1
Solve the systemby writing it as a matrix equation and using the inverse of the coefficient matrix. (Before starting, multiply the first two equations by 100 to eliminate decimals. Also, see Problem
In Problems write each system as a matrix equation and solve using inverses.x1 + 3x2 = k12x1 + 7x2 = k2(A) k1 = 2, k2 = –1(B) k1 = 1, k2 = 0(C) k1 = 3, k2 = –1
Solve Problem 34 by Gauss–Jordan elimination.Data from Problem 34Solve the systemby writing it as a matrix equation and using the inverse of the coefficient matrix. (Before starting, multiply the
In Problems write each system as a matrix equation and solve using inverses. = k₁ x₂ + x3 = K₂ 2x1 x₂ + 4x3 = K3 k3 (A) k₁= 1, K₂ = 0, k3 = 2 (B) k₁-1, K₂ = 1, k3 = 0 (C) k₁= 2,
In Problems write each system as a matrix equation and solve using inverses. = k₁ X3 = K₂ X1 + 2x3 = k3 (A) k₁ = 2, k₂ = 0, K3 = 4 (B) k₁ = 0, k₂= 4, k3 = -2 (C) k₁ = 4, k₂ = 2,
The economy of a small island nation is based on two sectors, agriculture and tourism. Production of a dollar’s worth of agriculture requires an input of $0.20 from agriculture and $0.15 from
(A) Set up Problem 41 as a matrix equation and solve using the inverse of the coefficient matrix.(B) Solve Problem 41 as in part (A) if 7.5 tons of nickel and 7 tons of copper are needed.Data from
An economy is based on three sectors, agriculture, manufacturing, and energy. Production of a dollar’s worth of agriculture requires inputs of $0.20 from agriculture, $0.20 from manufacturing, and
Solve Problem 46 by using a matrix equation and the inverse of the coefficient matrix.Data from Problem 46A person has $5,000 to invest, part at 5% and the rest at 10%. How much should be invested at
Discuss the effect on the solutions to Problem 49 if it is no longer required to have an equal number of $8 tickets and $20 tickets.Data from Problem 49An outdoor amphitheater has 25,000 seats.
In Problem explain why the system cannot be solved by matrix inverse methods. Discuss methods that could be used and then solve the system.x1 – 3x2 – 2x3 = –1 –2x1 + 6x2 + 4x3 = 3
In Problem explain why the system cannot be solved by matrix inverse methods. Discuss methods that could be used and then solve the system.x1 – 2x2 + 3x3 = 12x1 – 3x2 – 2x3 = 3x1 – x2 – 5x3
In Problem 46, is it possible to have an annual yield of $200? Of $600? Describe all possible annual yields.Data from Problem 46A person has $5,000 to invest, part at 5% and the rest at 10%. How much
An economy is based on two industrial sectors, agriculture and fabrication. Production of a dollar’s worth of agriculture requires an input of $0.30 from the agriculture sector and $0.20 from the
For n × n matrices A and B, and n × 1 column matrices C, D, and X, solve each matrix equation in Problem for X. Assume that all necessary inverses exist.AX – BX = C
For n × n matrices A and B, and n × 1 column matrices C, D, and X, solve each matrix equation in Problem for X. Assume that all necessary inverses exist.AX + BX = C
Solve Problem using augmented matrix methods.x1 – 2x2 = 12x1 – x2 = 5
Solve Problem using augmented matrix methods.x1 – 4x2 = –2–2x1 + x2 = –3
Solve Problem using augmented matrix methods.3x1 – x2 = 2x1 + 2x2 = 10
Solve Problem using augmented matrix methods.x1 + 2x2 = 42x1 + 4x2 = –8
Solve Problem using augmented matrix methods.2x1 + x2 = 6x1 – x2 = 3
Solve Problem using augmented matrix methods.3x1 – 6x2 = –9–2x1 + 4x2 = 6
Solve Problem using augmented matrix methods.4x1 – 2x2 = 2–6x1 + 3x2 = –3
Show that (A–1)–1 = A for: A = 4 [3 3 2
Solve Problem using augmented matrix methods.2x1 + x2 = 14x1 – x2 = –7
Find a, b, and c so that the graph of the quadratic equation y = ax2 + bx + c passes through the points (–2, 9), (1, –9), and (4, 9).
Solve Problem using augmented matrix methods.4x1 – 6x2 = 8–6x1 + 9x2 = –10
Refer to the encoding matrixEncode the message “WINGARDIUM LEVIOSA” using matrix A. A -11 2 3
Solve Problem using augmented matrix methods.–4x1 + 6x2 = –86x1 – 9x2 = 12
Refer to Problem 75. The cost of leasing an 8,000-gallon tank car is $450 per month, a 16,000-gallon tank car is $650 per month, and a 24,000-gallon tank car is $1,150 per month. Which of the
Solve Problem using augmented matrix methods.3x1 + 2x2 = 42x1 – x2 = 5
Refer to the encoding matrixEncode the message “FINITE INCANTATEM” using matrix A. A -11 2 3
Problem require the use of a graphing calculator or a computer. Use the 5 × 5 encoding matrix C given below. Form a matrix with 5 rows and as many columns as necessary to accommodate the
Problem require the use of a graphing calculator or a computer. Use the 5 × 5 encoding matrix C given below. Form a matrix with 5 rows and as many columns as necessary to accommodate the

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