Question 1

Use a graphing utility to find the point(s) of intersection of the graphs.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 2

Sketch the graph of the solution set of each system of inequalities.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 3

Use the statements below to write a system of equations.Solve the system by elimination. The sum of twice a number   and a number   is -14.The difference of   and   is 2.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 4

Sketch the graph of the inequality below.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 5

One acetic acid solution is 60% water and another is 40% water.How many liters of each solution should be mixed to produce 20 liters of a solution that is 49% water?

Accepted Answer

A)  5 liters of the 60% solution and 15 liters of the 40% solution 
B)  9 liters of the 60% solution and 11 liters of the 40% solution 
C)  15 liters of the 60% solution and 5 liters of the 40% solution 
D)  6 liters of the 60% solution and 14 liters of the 40% solution 
E)  14 liters of the 60% solution and 6 liters of the 40% solution 
A)  5 liters of the 60% solution and 15 liters of the 40% solution 
B)  9 liters of the 60% solution and 11 liters of the 40% solution 
C)  15 liters of the 60% solution and 5 liters of the 40% solution 
D)  6 liters of the 60% solution and 14 liters of the 40% solution 
E)  14 liters of the 60% solution and 6 liters of the 40% solution

Question 6

You invest $3700 in a fishing lure business.A lure costs $1.60 to produce and will be sold for $6.20.How many lures must you sell to break even?

Accepted Answer

A)  1716 lures 
B)  805 lures 
C)  2313 lures 
D)  475 lures 
E)  597 lures 
A)  1716 lures 
B)  805 lures 
C)  2313 lures 
D)  475 lures 
E)  597 lures

Question 7

An accounting firm charges $2500 for an audit and $350 for a tax return.Research and available resources have indicated the following constraints. The firm has 900 hours of staff time available each week.
The firm has 155 hours of review time available each week.
Each audit requires 75 hours of staff time and 10 hours of review time.
Each tax return requires 12.5 hours of staff time and 2.5 hours of review time.
The accounting firm lowers its charge for an audit to $2000.What numbers of audits and tax returns will bring in an optimal revenue?

Accepted Answer

A)  The optimal revenue will be $24,700 if the firms does 5 audits and 42 tax returns each week. 
B)  The optimal revenue will be $24,000 if the firms does 12 audits and 0 tax returns each week. 
C)  The optimal revenue will be $21,700 if the firms does 0 audits and 62 tax returns each week. 
D)  The optimal revenue will be $0 if the firms does 0 audits and 0 tax returns each week. 
E)  The optimal revenue will be $30,000 if the firms does 12 audits and 0 tax returns each week. 
A)  The optimal revenue will be $24,700 if the firms does 5 audits and 42 tax returns each week. 
B)  The optimal revenue will be $24,000 if the firms does 12 audits and 0 tax returns each week. 
C)  The optimal revenue will be $21,700 if the firms does 0 audits and 62 tax returns each week. 
D)  The optimal revenue will be $0 if the firms does 0 audits and 0 tax returns each week. 
E)  The optimal revenue will be $30,000 if the firms does 12 audits and 0 tax returns each week.

Question 8

A manufacturer produces two models of bicycles.The times (in hours) required for assembling, painting, and packaging each model are shown in the table. Process   The total times available for assembling, painting, and packing are 4000 hours, 4800 hours, and 1500 hours, respectively.The profit per unit are $50 for model A and $75 for model B.What is the optimal production level for each model? What is the optimal profit?

Accepted Answer

A)  The optimal profit of $120,000 occurs when no units of model A and 1600 units of of model B are produced. 
B)  The optimal profit of $112,000 occurs when no units of model A and 1000 units of of model B are produced. 
C)  The optimal profit of $97,500 occurs when no units of model A and 600 units of of model B are produced. 
D)  The optimal profit of $60,000 occurs when no units of model A and 0 units of of model B are produced. 
E)  The optimal profit of $112,000 occurs when no units of model A and 750 units of of model B are produced. 
A)  The optimal profit of $120,000 occurs when no units of model A and 1600 units of of model B are produced. 
B)  The optimal profit of $112,000 occurs when no units of model A and 1000 units of of model B are produced. 
C)  The optimal profit of $97,500 occurs when no units of model A and 600 units of of model B are produced. 
D)  The optimal profit of $60,000 occurs when no units of model A and 0 units of of model B are produced. 
E)  The optimal profit of $112,000 occurs when no units of model A and 750 units of of model B are produced.

Question 9

Graph the solution set of the system of inequalities below.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 10

Which of the following vertices of the constraint region shown is a minimum value of the objective function below.

Accepted Answer

A)  vertices C and D 
B)  only vertex C 
C)  only vertex A 
D)  vertices B and C 
E)  only vertex D 
A)  vertices C and D 
B)  only vertex C 
C)  only vertex A 
D)  vertices B and C 
E)  only vertex D

Question 11

Find an equation of the form   whose graph passes through the points     and

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 12

Use back-substitution to solve the system of linear equations.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 13

Solve the system by the method of substitution.

Accepted Answer

A)  (2, 1), (-1, -2) 
B)  (2, 3), (-1, 0) 
C)  (2, -1), (-1, -4) 
D)  (2, -1) 
E)  no real solution 
A)  (2, 1), (-1, -2) 
B)  (2, 3), (-1, 0) 
C)  (2, -1), (-1, -4) 
D)  (2, -1) 
E)  no real solution

Question 14

Determine which ordered pair is a solution of the system.

Accepted Answer

A)    
B)    
C)  (-9, 86) 
D)    
E)  (-9, 17) 
A)    
B)    
C)  (-9, 86) 
D)    
E)  (-9, 17)

Question 15

A farming cooperative mixes two brands of cattle feed.Brand X costs $30 per bag, and brand Y costs $25 per bag.Research and available resources have indicated the following constraints. Brand X contains two units nutritional element A, two units of element B, and two units of element C.
Brand Y contains one unit of nutritional element A, nine units of element B, and three units of element C.
The minimum requirements for nutrients A, B, and C are 12 units, 36 units, and 24 units, respectively.
What is the optimal number of bags of each brand that should be mixed? What is optimal cost?

Accepted Answer

A)  To minimize cost, use three bags of brands X and six bags of brand Y for optimal an cost of $540. 
B)  To minimize cost, use three bags of brands X and six bags of brand Y for optimal an cost of $320. 
C)  To minimize cost, use three bags of brands X and six bags of brand Y for optimal an cost of $240. 
D)  To minimize cost, use three bags of brands X and six bags of brand Y for optimal an cost of $300. 
E)  To minimize cost, use three bags of brands X and six bags of brand Y for optimal an cost of $360. 
A)  To minimize cost, use three bags of brands X and six bags of brand Y for optimal an cost of $540. 
B)  To minimize cost, use three bags of brands X and six bags of brand Y for optimal an cost of $320. 
C)  To minimize cost, use three bags of brands X and six bags of brand Y for optimal an cost of $240. 
D)  To minimize cost, use three bags of brands X and six bags of brand Y for optimal an cost of $300. 
E)  To minimize cost, use three bags of brands X and six bags of brand Y for optimal an cost of $360.

Question 16

Find the minimum and maximum values of the objective function and where they occur, subject to the indicated constraints. Objective function:   Constraints:

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

Find the consumer surplus for the pair of demand and supply equations below.

Accepted Answer

A)  $1,250,000 
B)  $3,750,000 
C)  $5,000,000 
D)  $2,500,000 
E)  $1,875,000 
A)  $1,250,000 
B)  $3,750,000 
C)  $5,000,000 
D)  $2,500,000 
E)  $1,875,000

Question 18

Solve the system of equations below, if possible.

Accepted Answer

A)    
B)    
C)    
D)    
E)  The system is inconsistent. 
A)    
B)    
C)    
D)    
E)  The system is inconsistent.

Question 19

Determine which one of the ordered triples below is a solution of the given system of equations.

Accepted Answer

A)  (7, 5, 17) 
B)  (-3, -2, 6) 
C)  (-2, -6, 3) 
D)  (7, 5, 6) 
E)  (6, -2, -3) 
A)  (7, 5, 17) 
B)  (-3, -2, 6) 
C)  (-2, -6, 3) 
D)  (7, 5, 6) 
E)  (6, -2, -3)

Question 20

For the given supply and demand equations, find the consumer surplus. Round to the nearest dollar. Demand Supply
P = 170 - 0.00003x p = 140 + 0.00004x

Accepted Answer

A)  $2,755,102 
B)  $3,030,612 
C)  $3,306,122 
D)  $4,132,653 
E)  $3,673,469 
A)  $2,755,102 
B)  $3,030,612 
C)  $3,306,122 
D)  $4,132,653 
E)  $3,673,469

Use a graphing utility to find the point(s) of intersection of the graphs.

Sketch the graph of the solution set of each system of inequalities.

Use the statements below to write a system of equations.Solve the system by elimination. The sum of twice a number and a number is -14.The difference of and is 2.

Sketch the graph of the inequality below.

One acetic acid solution is 60% water and another is 40% water.How many liters of each solution should be mixed to produce 20 liters of a solution that is 49% water?

You invest $3700 in a fishing lure business.A lure costs $1.60 to produce and will be sold for $6.20.How many lures must you sell to break even?

Graph the solution set of the system of inequalities below.

Which of the following vertices of the constraint region shown is a minimum value of the objective function below.

Find an equation of the form whose graph passes through the points and

Use back-substitution to solve the system of linear equations.

Solve the system by the method of substitution.

Determine which ordered pair is a solution of the system.

Find the minimum and maximum values of the objective function and where they occur, subject to the indicated constraints. Objective function: Constraints:

Find the consumer surplus for the pair of demand and supply equations below.

Solve the system of equations below, if possible.

Determine which one of the ordered triples below is a solution of the given system of equations.

For the given supply and demand equations, find the consumer surplus. Round to the nearest dollar. Demand Supply P = 170 - 0.00003x p = 140 + 0.00004x

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Matrices and Determinants

Sequences, Series, and Probability

Filters

Exam 5: Systems of Equations and Inequalities

Use a graphing utility to find the point(s) of intersection of the graphs.

Sketch the graph of the solution set of each system of inequalities.

Use the statements below to write a system of equations.Solve the system by elimination. The sum of twice a number and a number is -14.The difference of and is 2.

Sketch the graph of the inequality below.

One acetic acid solution is 60% water and another is 40% water.How many liters of each solution should be mixed to produce 20 liters of a solution that is 49% water?

You invest $3700 in a fishing lure business.A lure costs $1.60 to produce and will be sold for $6.20.How many lures must you sell to break even?

Graph the solution set of the system of inequalities below.

Which of the following vertices of the constraint region shown is a minimum value of the objective function below.

Find an equation of the form whose graph passes through the points and

Use back-substitution to solve the system of linear equations.

Solve the system by the method of substitution.

Determine which ordered pair is a solution of the system.

Find the minimum and maximum values of the objective function and where they occur, subject to the indicated constraints. Objective function: Constraints:

Find the consumer surplus for the pair of demand and supply equations below.

Solve the system of equations below, if possible.

Determine which one of the ordered triples below is a solution of the given system of equations.

For the given supply and demand equations, find the consumer surplus. Round to the nearest dollar. Demand Supply P = 170 - 0.00003x p = 140 + 0.00004x

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Matrices and Determinants

Sequences, Series, and Probability

Filters