Question 1

Find the graphical solution of the inequality. ​
6x - 18 < 0
​

Accepted Answer

A)    
B)    
C)    
A)    
B)    
C)

Question 2

Determine graphically the solution set for the system of inequalities. ​   ​

Accepted Answer

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

Question 3

Solve the following linear programming problem by the method of corners. Find the maximum and minimum of   subject to

Accepted Answer

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

Question 4

Determine graphically the solution set for the system of inequalities and indicate whether the solution set is bounded or unbounded. ​   ​

Accepted Answer

A)  unbounded   
B)  bounded  
​ 
C)  unbounded  
​ 
A)  unbounded   
B)  bounded  
​ 
C)  unbounded  
​

Question 5

Find the graphical solution of the inequality.

Accepted Answer

A)    
B)    
C)    
A)    
B)    
C)

Question 6

Find the optimal (maximum and minimum) values of the objective function on the feasible set   . ​   ​   ​

Accepted Answer

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

Question 7

Consider the production problem:   Find the shadow price for resource 2. Identify the binding and nonbinding constraints.

Accepted Answer

A)  The shadow price for resource 2 is $60 .Constraints 1, 2 and 3 are binding constraints. 
B)  The shadow price for resource 2 is $0.1 .Constraints 1 and 2 are binding constraints and constraint 3 is nonbinding. 
C)  The shadow price for resource 2 is $60 .Constraints 1 and 3 are nonbinding constraints and constraint 2 is binding. 
D)  The shadow price for resource 2 is $0.1 .Constraint 1 is binding constraint and constraints 2 and 3 are nonbinding. 
A)  The shadow price for resource 2 is $60 .Constraints 1, 2 and 3 are binding constraints. 
B)  The shadow price for resource 2 is $0.1 .Constraints 1 and 2 are binding constraints and constraint 3 is nonbinding. 
C)  The shadow price for resource 2 is $60 .Constraints 1 and 3 are nonbinding constraints and constraint 2 is binding. 
D)  The shadow price for resource 2 is $0.1 .Constraint 1 is binding constraint and constraints 2 and 3 are nonbinding.

Question 8

Solve the linear programming problem by the method of corners. Maximize   subject to

Accepted Answer

A)  x = 30, y = 38, P = 392 
B)  x = 20, y = 28, P = 344 
C)  x = 10, y = 38, P = 412 
D)  x = 30, y = 10, P = 300 
A)  x = 30, y = 38, P = 392 
B)  x = 20, y = 28, P = 344 
C)  x = 10, y = 38, P = 412 
D)  x = 30, y = 10, P = 300

Question 9

Determine graphically the solution set for the system of inequalities and indicate whether the solution set is bounded or unbounded. ​

Accepted Answer

A)  Unbounded   
B)  Unbounded   
C)  Unbounded   
A)  Unbounded   
B)  Unbounded   
C)  Unbounded

Question 10

Find the graphical solution of the inequality. ​   ​

Accepted Answer

A)    
B)    
C)    
A)    
B)    
C)

Question 11

Find the graphical solution of the inequality. ​   ​

Accepted Answer

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

Question 12

Find the graphical solution of the inequality. ​   ​

Accepted Answer

A)    
B)    
C)    
A)    
B)    
C)

Question 13

Solve the linear programming problem by the method of corners. Maximize   subject to

Accepted Answer

A)  x = 3; y = 4; P = 8 
B)  x = 3; y = 4; P = 7 
C)  x = 3; y =   ; P = 7 
D)  x = 4; y = 4; P = 7 
E)  x = 3; y = 5; P = 7 
A)  x = 3; y = 4; P = 8 
B)  x = 3; y = 4; P = 7 
C)  x = 3; y =   ; P = 7 
D)  x = 4; y = 4; P = 7 
E)  x = 3; y = 5; P = 7

Question 14

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. The following problem is a linear programming problem.
Minimize     subject to:   x - y = 0

Accepted Answer

A)  False.
As we know, a linear programming problem consists of a linear objective function to be maximized or minimized subject to certain constraints in the form of linear equalities or inequalities. The linear objective function to be minimized is C = 4x + 5y , but the constraint   are not in the form of linear inequality. 
B)  True.
As we know, a linear programming problem consists of a linear objective function to be maximized or minimized subject to certain constraints in the form of linear equalities or inequalities. The linear objective function to be minimized is C = 4x + 5y , and all the constraints   are in the form of linear equalities or inequalities. 
A)  False.
As we know, a linear programming problem consists of a linear objective function to be maximized or minimized subject to certain constraints in the form of linear equalities or inequalities. The linear objective function to be minimized is C = 4x + 5y , but the constraint   are not in the form of linear inequality. 
B)  True.
As we know, a linear programming problem consists of a linear objective function to be maximized or minimized subject to certain constraints in the form of linear equalities or inequalities. The linear objective function to be minimized is C = 4x + 5y , and all the constraints   are in the form of linear equalities or inequalities.

Question 15

Custom Office Furniture Company is introducing a new line of executive desks made from a specially selected grade of walnut. Initially, three different models-A, B, and C-are to be marketed. Each model A desk requires   hr for fabrication, 1 hr for assembly, and 1 hr for finishing; each model B desk requires   hr for fabrication, 1 hr for assembly, and 1 hr for finishing; each model C desk requires   hr,   hr, and   hr for fabrication, assembly, and finishing, respectively. The profit on each model A desk is $26, the profit on each model B desk is $28, and the profit on each model C desk is $24. The total time available in the fabrication department, the assembly department, and the finishing department in the first month of production is 240 hr, 160 hr, and 150 hr, respectively. To maximize Custom's profit, how many desks of each model should be made in the month?

Accepted Answer

A)  Maximize P = 26x + 28y + 24z subject to   
B)  Minimize P = 26x + 28y + 24z subject to   
C)  Maximize P = 26x + 28y + 24z subject to   
D)  Minimize P = 26x + 28y + 24z subject to   
E)  Minimize P = 26x + 28y + 24z subject to   
A)  Maximize P = 26x + 28y + 24z subject to   
B)  Minimize P = 26x + 28y + 24z subject to   
C)  Maximize P = 26x + 28y + 24z subject to   
D)  Minimize P = 26x + 28y + 24z subject to   
E)  Minimize P = 26x + 28y + 24z subject to

Question 16

Solve the following linear programming problem by the method of corners. ​
Maximize   ​
Subject to   ​

Accepted Answer

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

Question 17

You are given a linear programming problem.Use the method of corners to solve the problem. Minimize

Accepted Answer

A)  27 
B)  25 
C)  26 
D)  23 
E)  24 
A)  27 
B)  25 
C)  26 
D)  23 
E)  24

Question 18

Patricia has at most $36,000 to invest in securities in the form of corporate stocks. She has narrowed her choices to two groups of stocks: growth stocks that she assumes will yield a 11% return (dividends and capital appreciation) within a year and speculative stocks that she assumes will yield a 22% return (mainly in capital appreciation) within a year. Determine how much she should invest in each group of stocks in order to maximize the return on her investments within a year if she has decided to invest at least 3 times as much in growth stocks as in speculative stocks.

Accepted Answer

A)  $9,000 in growth stocks and $27,000 in speculative stocks; maximum return: $6,930 
B)  $27,000 in growth stocks and $9,000 in speculative stocks; maximum return: $4,950 
C)  $26,000 in growth stocks and $10,000 in speculative stocks; maximum return: $5,060 
D)  $27,000 in growth stocks and $9,000 in speculative stocks; maximum return: $6,775 
A)  $9,000 in growth stocks and $27,000 in speculative stocks; maximum return: $6,930 
B)  $27,000 in growth stocks and $9,000 in speculative stocks; maximum return: $4,950 
C)  $26,000 in growth stocks and $10,000 in speculative stocks; maximum return: $5,060 
D)  $27,000 in growth stocks and $9,000 in speculative stocks; maximum return: $6,775

Question 19

Use the method of corners to solve the problem. Find the range of values that the coefficient of x can assume without changing the optimal solution.
Find the range of values that requirement 1 can assume.
Find the shadow price for requirement 1.
Identify the binding and nonbinding constraints.

Accepted Answer

A)  x = 6, y = 0, C = 18     3
Constraint 1 is binding; constraint 2 is nonbinding. 
B)  x = 6, y = 0, C = 18     3
Both constraints are nonbinding. 
C)  x = 0, y = 6, C = 7    
3
Both constraints are binding. 
D)  x = 5, y = 0, C = 18     3
Constraint 1 is binding; constraint 2 is nonbinding. 
A)  x = 6, y = 0, C = 18     3
Constraint 1 is binding; constraint 2 is nonbinding. 
B)  x = 6, y = 0, C = 18     3
Both constraints are nonbinding. 
C)  x = 0, y = 6, C = 7    
3
Both constraints are binding. 
D)  x = 5, y = 0, C = 18     3
Constraint 1 is binding; constraint 2 is nonbinding.

Question 20

Formulate but do not solve the following exercise as a linear programming problem. Kane Manufacturing has a division that produces two models of fireplace grates, model A and model B. To produce each model A grate requires 4 lb of cast iron and 6 min of labor. To produce each model B grate requires 5 lb of cast iron and 3 min of labor. The profit for each model A grate is $2.00, and the profit for each model B grate is $1.50. If 1,100 lb of cast iron and 20 hr of labor are available for the production of grates per day, how many grates of each model should the division produce per day in order to maximize Kane's profits?

Accepted Answer

A)  Minimize   subject to   
B)  Maximize   subject to   
C)  Maximize   subject to   
D)  Maximize   subject to   
E)  Minimize   subject to   
A)  Minimize   subject to   
B)  Maximize   subject to   
C)  Maximize   subject to   
D)  Maximize   subject to   
E)  Minimize   subject to

Find the graphical solution of the inequality. 6x - 18 < 0

Determine graphically the solution set for the system of inequalities.

Solve the following linear programming problem by the method of corners. Find the maximum and minimum of subject to

Determine graphically the solution set for the system of inequalities and indicate whether the solution set is bounded or unbounded.

Find the graphical solution of the inequality.

Find the optimal (maximum and minimum) values of the objective function on the feasible set .

Consider the production problem: Find the shadow price for resource 2. Identify the binding and nonbinding constraints.

Solve the linear programming problem by the method of corners. Maximize subject to

Determine graphically the solution set for the system of inequalities and indicate whether the solution set is bounded or unbounded.

Find the graphical solution of the inequality.

Find the graphical solution of the inequality.

Find the graphical solution of the inequality.

Solve the linear programming problem by the method of corners. Maximize subject to

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. The following problem is a linear programming problem. Minimize subject to: x - y = 0

Solve the following linear programming problem by the method of corners. Maximize Subject to

You are given a linear programming problem.Use the method of corners to solve the problem. Minimize

Use the method of corners to solve the problem. Find the range of values that the coefficient of x can assume without changing the optimal solution. Find the range of values that requirement 1 can assume. Find the shadow price for requirement 1. Identify the binding and nonbinding constraints.

Straight Lines and Linear Functions

Systems of Linear Equations and Matrices

Linear Programming: an Algebraic Approach

Mathematics of Finance

Sets and Counting

Probability

Probability Distributions and Statistics

Markov Chains and the Theory of Games

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Exam 3: Linear Programming: a Geometric Approach

Find the graphical solution of the inequality. ​ 6x - 18 < 0 ​

Determine graphically the solution set for the system of inequalities. ​ ​

Solve the following linear programming problem by the method of corners. Find the maximum and minimum of subject to

Determine graphically the solution set for the system of inequalities and indicate whether the solution set is bounded or unbounded. ​ ​

Find the graphical solution of the inequality.

Find the optimal (maximum and minimum) values of the objective function on the feasible set . ​ ​ ​

Consider the production problem: Find the shadow price for resource 2. Identify the binding and nonbinding constraints.

Solve the linear programming problem by the method of corners. Maximize subject to

Determine graphically the solution set for the system of inequalities and indicate whether the solution set is bounded or unbounded. ​

Find the graphical solution of the inequality. ​ ​

Find the graphical solution of the inequality. ​ ​

Find the graphical solution of the inequality. ​ ​

Solve the linear programming problem by the method of corners. Maximize subject to

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. The following problem is a linear programming problem. Minimize subject to: x - y = 0

Solve the following linear programming problem by the method of corners. ​ Maximize ​ Subject to ​

You are given a linear programming problem.Use the method of corners to solve the problem. Minimize

Use the method of corners to solve the problem. Find the range of values that the coefficient of x can assume without changing the optimal solution. Find the range of values that requirement 1 can assume. Find the shadow price for requirement 1. Identify the binding and nonbinding constraints.

Straight Lines and Linear Functions

Systems of Linear Equations and Matrices

Linear Programming: an Algebraic Approach

Mathematics of Finance

Sets and Counting

Probability

Probability Distributions and Statistics

Markov Chains and the Theory of Games

Filters

Find the graphical solution of the inequality. 6x - 18 < 0

Determine graphically the solution set for the system of inequalities.

Determine graphically the solution set for the system of inequalities and indicate whether the solution set is bounded or unbounded.

Find the optimal (maximum and minimum) values of the objective function on the feasible set .

Determine graphically the solution set for the system of inequalities and indicate whether the solution set is bounded or unbounded.

Find the graphical solution of the inequality.

Find the graphical solution of the inequality.

Find the graphical solution of the inequality.

Solve the following linear programming problem by the method of corners. Maximize Subject to