Question 1

Use technology to solve the problem. ​
Minimize   subject to
​   ​

Accepted Answer

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

Question 2

The Wellbuilt Company produces two types of wood chippers, economy and deluxe. The deluxe model requires 3 hours to assemble and 1 hour to paint, and the economy model requires 2 hours to assemble and 1.5 hour to paint. The maximum number of assembly hours available is 24 per day, and the maximum number of painting hours available is 15 per day. Let x represent the number of deluxe models and y represent the number of economy models. Graph the solution of the system of inequalities and find the corners of the solution region. ​

Accepted Answer

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

Question 3

A farm co-op has 6,001 acres available to plant with corn and soybeans. Each acre of corn requires 9 gallons of fertilizer/herbicide and 0.75 hour of labor to harvest. Each acre of soybeans requires 3 gallons of fertilizer/herbicide and 1 hour of labor to harvest. The co-op has available at most 40,500 gallons of fertilizer/herbicide and at most 5,250 hours of labor for harvesting. Find the maximum profit if the profits per acre are $75 for corn and $45 for soybeans. Round your answer to the nearest cent if necessary. ​

Accepted Answer

A) $236,250.00 
B) $393,750.00 
C) $202,500.00 
D) $382,530.00 
E) $335,472.97 
A) $236,250.00 
B) $393,750.00 
C) $202,500.00 
D) $382,530.00 
E) $335,472.97

Question 4

Assume that each nurse works 8 consecutive hours at the Beaver Medical Center. The center has the following staffing requirements for each 4-hour work period. ​   ​
If   represents the number of nurses starting in period 1,   the number starting in period 2, and so on, write and solve the linear programming problem that will minimize the total number of nurses needed. (Note that the nurses who begin work in period 6 work periods 6 and 1 for their 8-hour shift.)
​

Accepted Answer

A) The minimum 67 is nurses with 27 nurses starting in period 1, 5 nurses starting in period 2, 18 nurses starting in period 3, 10 nurses starting in period 4, and 7 nurses starting in period 5 (no nurses need to start in period 6). 
B) The minimum is 67 nurses with 27 nurses starting in period 1, 18 nurses starting in period 3, and 10 nurses starting in period 4, 7 nurses starting in period 5, and 5 nurses starting in period 6 (no nurses need to start in period 2). 
C) The minimum is 67 nurses with 32 nurses starting in period 1, 18 nurses starting in period 3, and 10 nurses starting in period 4, and 7 nurses starting in period 5 (no nurses need to start in periods 2 and 6). 
D) The minimum is 72 nurses with 32 nurses starting in period 1, 18 nurses starting in period 3, and 10 nurses starting in period 4, and 12 nurses starting in period 5 (no nurses need to start in periods 2 and 6). 
E) The minimum is 62 nurses with 32 nurses starting in period 1, 13 nurses starting in period 3, and 10 nurses starting in period 4, and 7 nurses starting in period 5 (no nurses need to start in periods 2 and 6). 
A) The minimum 67 is nurses with 27 nurses starting in period 1, 5 nurses starting in period 2, 18 nurses starting in period 3, 10 nurses starting in period 4, and 7 nurses starting in period 5 (no nurses need to start in period 6). 
B) The minimum is 67 nurses with 27 nurses starting in period 1, 18 nurses starting in period 3, and 10 nurses starting in period 4, 7 nurses starting in period 5, and 5 nurses starting in period 6 (no nurses need to start in period 2). 
C) The minimum is 67 nurses with 32 nurses starting in period 1, 18 nurses starting in period 3, and 10 nurses starting in period 4, and 7 nurses starting in period 5 (no nurses need to start in periods 2 and 6). 
D) The minimum is 72 nurses with 32 nurses starting in period 1, 18 nurses starting in period 3, and 10 nurses starting in period 4, and 12 nurses starting in period 5 (no nurses need to start in periods 2 and 6). 
E) The minimum is 62 nurses with 32 nurses starting in period 1, 13 nurses starting in period 3, and 10 nurses starting in period 4, and 7 nurses starting in period 5 (no nurses need to start in periods 2 and 6).

Question 5

A company manufactures two types of electric hedge trimmers, one of which is cordless. The cord-type trimmer requires 2 hours to make, and the cordless model requires 7 hours. The company has only 800 work hours to use in manufacturing each day, and the packaging department can package only 300 trimmers per day. Let x represent the number of cord type models and y represent the number of cordless models. Write the inequalities that describe the constraints on the number of each type of hedge trimmer produced. ​

Accepted Answer

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

Question 6

Use the simplex method to maximize the given function. Assume all variables are nonnegative. Maximize   subject to

Accepted Answer

A) maximum: 126 at  
,  
,   
B) maximum: 337 at  
,  
,   
C) maximum: 386 at  
,  
,   
D) maximum: 43 at  
,  
,   
E) maximum: 368 at  
,  
,   
A) maximum: 126 at  
,  
,   
B) maximum: 337 at  
,  
,   
C) maximum: 386 at  
,  
,   
D) maximum: 43 at  
,  
,   
E) maximum: 368 at  
,  
,

Question 7

Use the rules of exponents to simplify the expression.   ​

Accepted Answer

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

Question 8

The Janie Gioffre Drapery Company makes three types of draperies at two different locations. At location I, it can make 10 pairs of deluxe drapes, 20 pairs of better drapes, and 13 pairs of standard drapes per day. At location II, it can make 20 pairs of deluxe drapes, 50 pairs of better drapes, and 6 pairs of standard drapes per day. The company has orders for 2,000 pairs of deluxe drapes, 4,200 pairs of better drapes, and 1,200 pairs of standard drapes. If the daily costs are $700 per day at location I and $800 per day at location II, how many days should Janie schedule at each location in order to fill the orders at minimum cost? Find the minimum cost. Round your answers to the nearest whole number if necessary. ​

Accepted Answer

A) Minimum cost of $160,000 occurs with 0 days at location I and 200 days at location II. 
B) Minimum cost of $140,000 occurs with 200 days at location I and 0 days at location II. 
C) Minimum cost of $97,000 occurs with 70 days at location I and 60 days at location II. 
D) Minimum cost of $128,000 occurs with 160 days at location I and 20 days at location II. 
E) Minimum cost of $98,000 occurs with 60 days at location I and 70 days at location II. 
A) Minimum cost of $160,000 occurs with 0 days at location I and 200 days at location II. 
B) Minimum cost of $140,000 occurs with 200 days at location I and 0 days at location II. 
C) Minimum cost of $97,000 occurs with 70 days at location I and 60 days at location II. 
D) Minimum cost of $128,000 occurs with 160 days at location I and 20 days at location II. 
E) Minimum cost of $98,000 occurs with 60 days at location I and 70 days at location II.

Question 9

Graph the solution of the system of inequalities. ​   ​

Accepted Answer

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

Question 10

Solve the following linear programming problem. ​
Minimize   subject to
​   ​

Accepted Answer

A) ​1,485 
B) ​825 
C) ​1,890 
D) ​1,050 
E) ​630 
A) ​1,485 
B) ​825 
C) ​1,890 
D) ​1,050 
E) ​630

Question 11

In a laboratory experiment, two separate foods are given to experimental animals. Each food contains essential ingredients, A and B, for which the animals have a minimum requirement, and each food also has an ingredient C, which can be harmful to the animals. The table below summarizes this information. ​   ​
Determine how many grams of foods 1 and 2 should be given in order to satisfy the requirements for A and B while minimizing the amount of ingredient C ingested. Also determine the minimum amount of ingredient C ingested. Round your answer to one decimal place if necessary.
​

Accepted Answer

A) 11 grams of food 1 and 0 gram0 of food 2 satisfy the minimum requirements for A and B while minimizing the amount of ingredient C to 11 grams. 
B) ​0 gram0 of food 1 and 11 grams of food 2 satisfy the minimum requirements for A and B while minimizing the amount of ingredient C to 11 grams. 
C) ​12 grams of food 1 and 0 gram0 of food 2 satisfy the minimum requirements for A and B while minimizing the amount of ingredient C to 60 grams. 
D) ​1 gram0 of food 1 and 11 grams of food 2 satisfy the minimum requirements for A and B while minimizing the amount of ingredient C to 16 grams. 
E) ​2 grams of food 1 and 11 grams of food 2 satisfy the minimum requirements for A and B while minimizing the amount of ingredient C to 21 grams. 
A) 11 grams of food 1 and 0 gram0 of food 2 satisfy the minimum requirements for A and B while minimizing the amount of ingredient C to 11 grams. 
B) ​0 gram0 of food 1 and 11 grams of food 2 satisfy the minimum requirements for A and B while minimizing the amount of ingredient C to 11 grams. 
C) ​12 grams of food 1 and 0 gram0 of food 2 satisfy the minimum requirements for A and B while minimizing the amount of ingredient C to 60 grams. 
D) ​1 gram0 of food 1 and 11 grams of food 2 satisfy the minimum requirements for A and B while minimizing the amount of ingredient C to 16 grams. 
E) ​2 grams of food 1 and 11 grams of food 2 satisfy the minimum requirements for A and B while minimizing the amount of ingredient C to 21 grams.

Question 12

Convert the constraint inequalities   and   to equations containing slack variables.

Accepted Answer

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

Question 13

An ice cream company is planning its production for next week. Demand for premium and light ice creams continues to outpace the company's production capacities. Two resources used in ice cream production are in short supply for next week. The mixing machine will be available for only 150 hours, and only 30000 gallons of high grade milk will be available. One hundred gallons of premium ice-cream requires 0.6 hour of mixing and 180 gallons of milk. One hundred gallons of light ice cream requires 1 hour of mixing and 140 gallons of milk. If company earns a profit of $100 per hundred gallons on both of its ice creams, how many gallons of premium and of light ice cream should company produce next week to maximize profit? How much profit will result? Round your profit to the nearest cent and another answers - to the nearest whole number. ​

Accepted Answer

A) The company should produce 94 gallons of premium and 94 gallons of light ice cream to maximize the profit. The resultant maximum profit is $15,000.00 . 
B) The company should produce 94 gallons of premium and 94 gallons of light ice cream to maximize the profit. The resultant maximum profit is $18,750.00. 
C) The company should produce 94 gallons of premium and 94 gallons of light ice cream to maximize the profit. The resultant maximum profit is $16,666.67. 
D) The company should produce 69 gallons of premium and 69 gallons of light ice cream to maximize the profit. The resultant maximum profit is $13,800.00. 
E) The company should produce 119 gallons of premium and 119 gallons of light ice cream to maximize the profit. The resultant maximum profit is $23,800.00. 
A) The company should produce 94 gallons of premium and 94 gallons of light ice cream to maximize the profit. The resultant maximum profit is $15,000.00 . 
B) The company should produce 94 gallons of premium and 94 gallons of light ice cream to maximize the profit. The resultant maximum profit is $18,750.00. 
C) The company should produce 94 gallons of premium and 94 gallons of light ice cream to maximize the profit. The resultant maximum profit is $16,666.67. 
D) The company should produce 69 gallons of premium and 69 gallons of light ice cream to maximize the profit. The resultant maximum profit is $13,800.00. 
E) The company should produce 119 gallons of premium and 119 gallons of light ice cream to maximize the profit. The resultant maximum profit is $23,800.00.

Question 14

Set up the simplex matrix used to solve the linear programming problem. Assume all variables are nonnegative. ​
Maximize   subject to
​   ​

Accepted Answer

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

Question 15

Suppose a sausage company makes two different kinds of hot dogs, regular and all beef. Each pound of all-beef hot dogs requires 0.75 lb of beef and 0.2 lb of spices, and each pound of regular hot dogs requires 0.18 lb of beef, 0.3 lb of pork, and 0.2 lb of spices. Suppliers can deliver at most 982.5 lb of beef, at most 600 lb of pork, and at least 490 lb of spices. If the profit is $0.60 on each pound of all-beef hot dogs and $0.40 on each pound of regular hot dogs, how many pounds of each should be produced to obtain maximum profit? What is the maximum profit?

Accepted Answer

A) Maxomize profit is $1,300 with 840 lbs of all - beef and 1,990 lbs of regular hot dogs. 
B) Maxomize profit is $1,344 with 840 lbs of all - beef and 2,100 lbs of regular hot dogs. 
C) Maxomize profit is $1,298 with 830 lbs of all - beef and 2,000 lbs of regular hot dogs. 
D) Maxomize profit is $1,532 with 2,000 lbs of all - beef and 830 lbs of regular hot dogs. 
E) Maxomize profit is $1,530 with 1,990 lbs of all - beef and 840 lbs of regular hot dogs. 
A) Maxomize profit is $1,300 with 840 lbs of all - beef and 1,990 lbs of regular hot dogs. 
B) Maxomize profit is $1,344 with 840 lbs of all - beef and 2,100 lbs of regular hot dogs. 
C) Maxomize profit is $1,298 with 830 lbs of all - beef and 2,000 lbs of regular hot dogs. 
D) Maxomize profit is $1,532 with 2,000 lbs of all - beef and 830 lbs of regular hot dogs. 
E) Maxomize profit is $1,530 with 1,990 lbs of all - beef and 840 lbs of regular hot dogs.

Question 16

A simplex matrix is given. In this case the solution is complete, so identify the maximum value of f and a set of values of the variables that gives this maximum value. If multiple solutions may exist, indicate this and locate the next pivot. ​   ​

Accepted Answer

A) The maximum value of f is 160 when  
,  
And  
) 
B) The maximum value of f is 160 when  
,  
And  
) 
C) The maximum value of f is 160 when  
,  
And  
) 
D) The maximum value of f is 160 when  
,  
) Since multiple solutions are possible, pivot on 1 in R4C​4. 
E) The maximum value of f is 160 when  
,  
) Since multiple solutions are possible, pivot on 2 in R3C5​. 
A) The maximum value of f is 160 when  
,  
And  
) 
B) The maximum value of f is 160 when  
,  
And  
) 
C) The maximum value of f is 160 when  
,  
And  
) 
D) The maximum value of f is 160 when  
,  
) Since multiple solutions are possible, pivot on 1 in R4C​4. 
E) The maximum value of f is 160 when  
,  
) Since multiple solutions are possible, pivot on 2 in R3C5​.

Question 17

A minimization problem is given. Solve its dual problem with the simplex method. ​
Minimize   subject to
​   ​

Accepted Answer

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

Question 18

A farm co-op has 6,008 acres available to plant with corn and soybeans. Each acre of corn requires 9 gallons of fertilizer/herbicide and 0.75 hour of labor to harvest. Each acre of soybeans requires 3 gallons of fertilizer/herbicide and 1hour of labor to harvest. The co-op has available at most 40,500 gallons of fertilizer/herbicide and at most 5,250 hours of labor for harvesting. Find the maximum profit if the profits per acre are $70 for corn and $55 for soybeans. Round your answer to the nearest cent if necessary. ​

Accepted Answer

A) $386,630.00 
B) $288,750.00 
C) $375,080.00 
D) $247,500.00 
E) $394,169.00 
A) $386,630.00 
B) $288,750.00 
C) $375,080.00 
D) $247,500.00 
E) $394,169.00

Question 19

A sausage company makes two different kinds of hot dogs, regular and all beef. Each pound of all-beef hot dogs requires 0.79 lb of beef and 0.24 lb of spices, and each pound of regular hot dogs requires 0.17 lb of beef, 0.34 lb of pork, and 0.22 lb of spices. Suppliers can deliver at most 1044 lb of beef, at most 402 lb of pork, and at least 300 lb of spices. Let x represent the number of pounds of regular meat and y represent the number of pounds of all beef. Graph the region determined by the constraint inequalities. ​

Accepted Answer

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

Question 20

The Video Star Company makes two different models of DVD players, which are assembled on two different assembly lines. Line 1 can assemble 32 units of the Star model and 44 units of the Prostar model per hour, and Line 2 can assemble 150 units of the Star model and 40 units of the Prostar model per hour. The company needs to produce at least 260 units of the Star model and 225 units of the Prostar model to fill an order. Let x represent the number of assembly hours for Line 1 and y represent the number of assembly hours for Line 2. Write the inequalities that describe the production constraints on the number of each type of DVD player needed to fill the order. ​

Accepted Answer

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

Use technology to solve the problem. Minimize subject to

Use the simplex method to maximize the given function. Assume all variables are nonnegative. Maximize subject to

Use the rules of exponents to simplify the expression.

Graph the solution of the system of inequalities.

Solve the following linear programming problem. Minimize subject to

Convert the constraint inequalities and to equations containing slack variables.

Set up the simplex matrix used to solve the linear programming problem. Assume all variables are nonnegative. Maximize subject to

A simplex matrix is given. In this case the solution is complete, so identify the maximum value of f and a set of values of the variables that gives this maximum value. If multiple solutions may exist, indicate this and locate the next pivot.

A minimization problem is given. Solve its dual problem with the simplex method. Minimize subject to

Algebraic Concepts

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability; Data Description

Derivatives

Applications of Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Exam 5: Inequalities and Linear Programming

Use technology to solve the problem. ​ Minimize subject to ​ ​

Use the simplex method to maximize the given function. Assume all variables are nonnegative. Maximize subject to

Use the rules of exponents to simplify the expression. ​

Graph the solution of the system of inequalities. ​ ​

Solve the following linear programming problem. ​ Minimize subject to ​ ​

Convert the constraint inequalities and to equations containing slack variables.

Set up the simplex matrix used to solve the linear programming problem. Assume all variables are nonnegative. ​ Maximize subject to ​ ​

A simplex matrix is given. In this case the solution is complete, so identify the maximum value of f and a set of values of the variables that gives this maximum value. If multiple solutions may exist, indicate this and locate the next pivot. ​ ​

A minimization problem is given. Solve its dual problem with the simplex method. ​ Minimize subject to ​ ​

Algebraic Concepts

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability; Data Description

Derivatives

Applications of Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Use technology to solve the problem. Minimize subject to

Use the rules of exponents to simplify the expression.

Graph the solution of the system of inequalities.

Solve the following linear programming problem. Minimize subject to

Set up the simplex matrix used to solve the linear programming problem. Assume all variables are nonnegative. Maximize subject to

A simplex matrix is given. In this case the solution is complete, so identify the maximum value of f and a set of values of the variables that gives this maximum value. If multiple solutions may exist, indicate this and locate the next pivot.

A minimization problem is given. Solve its dual problem with the simplex method. Minimize subject to