Question 1

Use the simplex method, Excel, or another technology to find the solution of the problem given below. Assume all variables are nonnegative. ​   ​

Accepted Answer

A)  Maximum is   
B)  Maximum is   
C)  Maximum is   
D)  Maximum is   
E)  Maximum is   
A)  Maximum is   
B)  Maximum is   
C)  Maximum is   
D)  Maximum is   
E)  Maximum is

Question 2

Form the simplex matrix for the problem given below. ​   ​

Accepted Answer

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

Question 3

Suppose a primal minimization problem and its dual maximization problem were solved by using the simplex method on the dual problem. The final simplex matrix is given. Find the solution of the minimization problem. Use y1, y2, y3 as the variables and g as the function. ​   ​

Accepted Answer

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

Question 4

The James MacGregor Mining Company owns three mines: I, II, and III. Three grades of ore, A, B, and C, are mined at these mines. For each grade of ore, the number of tons per week available from each mine and the number of tons per week required to fill orders are given in the following table. ​
 
​
Find the number of days that the company should operate each mine so that orders are filled at minimum cost. Find the minimum cost.
​
​

Accepted Answer

A)  Minimum cost is $54,000 obtained by operating mine I for 2 days, mine II for 2 days, and mine III for 2 days. 
B)  Minimum cost is $93,400 obtained by operating mine I for 3 days, mine II for 3 days, and mine III for 4 days. 
C)  Minimum cost is $83,600 obtained by operating mine I for 2 days, mine II for 4 days, and mine III for 3 days. 
D)  Minimum cost is $74,600 obtained by operating mine I for 4 days, mine II for 3 days, and mine III for 2 days. 
E)  Minimum cost is $78,400 obtained by operating mine I for 4 days, mine II for 2 days, and mine III for 3 days. 
A)  Minimum cost is $54,000 obtained by operating mine I for 2 days, mine II for 2 days, and mine III for 2 days. 
B)  Minimum cost is $93,400 obtained by operating mine I for 3 days, mine II for 3 days, and mine III for 4 days. 
C)  Minimum cost is $83,600 obtained by operating mine I for 2 days, mine II for 4 days, and mine III for 3 days. 
D)  Minimum cost is $74,600 obtained by operating mine I for 4 days, mine II for 3 days, and mine III for 2 days. 
E)  Minimum cost is $78,400 obtained by operating mine I for 4 days, mine II for 2 days, and mine III for 3 days.

Question 5

A simplex matrix for a standard maximization problem is given. Indicate whether or not the solution shown is complete (optimal). If the solution is not complete, find the next pivot or indicate that no solution exists. ​   ​

Accepted Answer

A)  next pivot: 1 in R4C3 
B)  next pivot: -2 in R4C5 
C)  next pivot: 7 in R2C5 
D)  optimal solution 
E)  no solution 
A)  next pivot: 1 in R4C3 
B)  next pivot: -2 in R4C5 
C)  next pivot: 7 in R2C5 
D)  optimal solution 
E)  no solution

Question 6

Find the transpose of the matrix associated with the given minimization problem. y ​
Minimize   subject to
​   ​

Accepted Answer

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

Question 7

Graph the solution of the system of inequalities. ​   ​

Accepted Answer

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

Question 8

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 9

Use the simplex method, Excel, or another technology, to find the solution of the problem given below. Assume all variables are nonnegative. ​   ​

Accepted Answer

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

Question 10

Use the simplex method to find the optimal solution. ​
Minimize   subject to   ​

Accepted Answer

A)  minimum:   
B)  minimum:   
C)  minimum:   
D)  minimum:   
E)  minimum:   
A)  minimum:   
B)  minimum:   
C)  minimum:   
D)  minimum:   
E)  minimum:

Question 11

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 12

Graph the solution of the system of inequalities. ​   ​

Accepted Answer

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

Question 13

Use the simplex method, Excel, or another technology to solve.​ ​   ​

Accepted Answer

A)  minimum:   
B)  minimum:   
C)  minimum:   
D)  minimum:   
E)  minimum:   
A)  minimum:   
B)  minimum:   
C)  minimum:   
D)  minimum:   
E)  minimum:

Question 14

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 15

Use the simplex method to maximize the function (if possible) subject to the given constraints. If there is no solution, indicate this; if multiple solutions exist, give one solution. ​
Maximize   subject to
​   ​

Accepted Answer

A)  maximum: 384 at   ,   
B)  maximum: 336 at   ,   
C)  maximum: 224 at   ,   
D)  maximum: 336 at   ,   
E)  no solution 
A)  maximum: 384 at   ,   
B)  maximum: 336 at   ,   
C)  maximum: 224 at   ,   
D)  maximum: 336 at   ,   
E)  no solution

Question 16

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)

Question 17

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

Accepted Answer

A)  20 
B)  64 
C)  24 
D)  84 
E)  70 
A)  20 
B)  64 
C)  24 
D)  84 
E)  70

Question 18

Use the given feasible region determined by the constraint inequalities to find the maximum and minimum of the given objective function (if they exist). ​   ​   ​

Accepted Answer

A)  max: 110, min: 24 
B)  max: 52, min: 11 
C)  max: 11, min: 17 
D)  max: 46, min: 11 
E)  do not exist 
A)  max: 110, min: 24 
B)  max: 52, min: 11 
C)  max: 11, min: 17 
D)  max: 46, min: 11 
E)  do not exist

Question 19

Write the dual maximization problem. Be sure to rename the variables. ​
Minimize   subject to
​   ​

Accepted Answer

A)  Maximize  
Constraints:   
B)  Maximize  
Constraints:   ​ 
C)  ​Maximize  
Constraints:   
D)  Maximize  
Constraints:   
E)  Maximize  
Constraints:   
A)  Maximize  
Constraints:   
B)  Maximize  
Constraints:   ​ 
C)  ​Maximize  
Constraints:   
D)  Maximize  
Constraints:   
E)  Maximize  
Constraints:

Question 20

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)

Use the simplex method, Excel, or another technology to find the solution of the problem given below. Assume all variables are nonnegative.

Form the simplex matrix for the problem given below.

Suppose a primal minimization problem and its dual maximization problem were solved by using the simplex method on the dual problem. The final simplex matrix is given. Find the solution of the minimization problem. Use y₁, y₂, y₃ as the variables and g as the function.

A simplex matrix for a standard maximization problem is given. Indicate whether or not the solution shown is complete (optimal). If the solution is not complete, find the next pivot or indicate that no solution exists.

Find the transpose of the matrix associated with the given minimization problem. y Minimize subject to

Graph the solution of the system of inequalities.

Use the simplex method, Excel, or another technology, to find the solution of the problem given below. Assume all variables are nonnegative.

Use the simplex method to find the optimal solution. Minimize subject to

Graph the solution of the system of inequalities.

Use the simplex method, Excel, or another technology to solve.

Convert the constraint inequalities and to equations containing slack variables.

Use the simplex method to maximize the function (if possible) subject to the given constraints. If there is no solution, indicate this; if multiple solutions exist, give one solution. Maximize subject to

Solve the following linear programming problem. Maximize subject to

Use the given feasible region determined by the constraint inequalities to find the maximum and minimum of the given objective function (if they exist).

Write the dual maximization problem. Be sure to rename the variables. Minimize subject to

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability and Data Description

Derivatives

Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals - Techniques

A: Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

Filters

Exam 4: Inequalities and Linear Programming

Use the simplex method, Excel, or another technology to find the solution of the problem given below. Assume all variables are nonnegative. ​ ​

Form the simplex matrix for the problem given below. ​ ​

Suppose a primal minimization problem and its dual maximization problem were solved by using the simplex method on the dual problem. The final simplex matrix is given. Find the solution of the minimization problem. Use y1, y2, y3 as the variables and g as the function. ​ ​

A simplex matrix for a standard maximization problem is given. Indicate whether or not the solution shown is complete (optimal). If the solution is not complete, find the next pivot or indicate that no solution exists. ​ ​

Find the transpose of the matrix associated with the given minimization problem. y ​ Minimize subject to ​ ​

Graph the solution of the system of inequalities. ​ ​

Use the simplex method, Excel, or another technology, to find the solution of the problem given below. Assume all variables are nonnegative. ​ ​

Use the simplex method to find the optimal solution. ​ Minimize subject to ​

Graph the solution of the system of inequalities. ​ ​

Use the simplex method, Excel, or another technology to solve.​ ​ ​

Convert the constraint inequalities and to equations containing slack variables. ​

Use the simplex method to maximize the function (if possible) subject to the given constraints. If there is no solution, indicate this; if multiple solutions exist, give one solution. ​ Maximize subject to ​ ​

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

Use the given feasible region determined by the constraint inequalities to find the maximum and minimum of the given objective function (if they exist). ​ ​ ​

Write the dual maximization problem. Be sure to rename the variables. ​ Minimize subject to ​ ​

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability and Data Description

Derivatives

Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals - Techniques

A: Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

Filters

Use the simplex method, Excel, or another technology to find the solution of the problem given below. Assume all variables are nonnegative.

Form the simplex matrix for the problem given below.

Suppose a primal minimization problem and its dual maximization problem were solved by using the simplex method on the dual problem. The final simplex matrix is given. Find the solution of the minimization problem. Use y₁, y₂, y₃ as the variables and g as the function.

A simplex matrix for a standard maximization problem is given. Indicate whether or not the solution shown is complete (optimal). If the solution is not complete, find the next pivot or indicate that no solution exists.

Find the transpose of the matrix associated with the given minimization problem. y Minimize subject to

Graph the solution of the system of inequalities.

Use the simplex method, Excel, or another technology, to find the solution of the problem given below. Assume all variables are nonnegative.

Use the simplex method to find the optimal solution. Minimize subject to

Graph the solution of the system of inequalities.

Use the simplex method, Excel, or another technology to solve.

Convert the constraint inequalities and to equations containing slack variables.

Use the simplex method to maximize the function (if possible) subject to the given constraints. If there is no solution, indicate this; if multiple solutions exist, give one solution. Maximize subject to

Solve the following linear programming problem. Maximize subject to

Use the given feasible region determined by the constraint inequalities to find the maximum and minimum of the given objective function (if they exist).

Write the dual maximization problem. Be sure to rename the variables. Minimize subject to