Question 1

Use the method of substitution to solve the system. 
A) 
B) 
C) 
D) 
E)no solution

Accepted Answer

B

Question 2

A stationary company makes two types of notebooks: a deluxe notebook with subject dividers, which sells for $1.1, and a regular notebook, which sells for $0.85. The production cost is $1.00 for each deluxe notebook and $0.75 for each regular notebook. The company has the facilities to manufacture between 2,000 and 3,000 deluxe and between 3,000 and 6,000 regular notebooks, but not more than 7,000 altogether. How many notebooks of each type should be manufactured to maximize the difference between the selling prices and the production cost?
A)2,000 deluxe and 5,000 regular
B)3,000 deluxe and 4,000 regular
C)2,300 deluxe and 4,000 regular
D)2,500 deluxe and 4,000 regular
E)3,000 deluxe and 5,000 regular

Accepted Answer

To maximize the difference between selling prices and production costs, the company should produce the maximum number of deluxe notebooks (3,000) due to their higher profit margin ($0.10 each) compared to regular notebooks ($0.10 each as well), but with a higher selling price. The remaining capacity (up to 7,000 notebooks in total) should be filled with regular notebooks, which is 4,000 in this case.

Question 3

Solve the system  using the inverse method.
A) 
B) 
C) 
D)The system is inconsistent
E)The equations are dependent

Accepted Answer

A

Question 4

Solve the system. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Solve the system. 
A) 
B) 
C) 
D)...

Question 5

Solve the system  using the inverse method.
A) 
B) 
C) 
D)The system is inconsistent
E)The equations are dependent

Accepted Answer

The answer of Solve the system  using the inverse...

Question 6

Find the inverse of the matrix if it exists. 
A) 
B) 
C) 
D) 
E)Does not exist

Accepted Answer

The answer of Find the inverse of the matrix if...

Question 7

A manufacturer of cell phones makes a profit of $23 on a deluxe model and $31 on a standard model. The company wishes to produce at least 80 deluxe models and at least 100 standard models per day. To maintain high quality, the daily production should not exceed 240 phones. How many of each type should be produced daily in order to maximize the profit?
A)31 standard and 80 deluxe
B)80 standard and 160 deluxe
C)160 standard and 80 deluxe
D)200 standard and 40 deluxe
E)160 standard and 60 deluxe

Accepted Answer

To maximize profit, the company should produce as many units as possible of the model that generates the highest profit per unit, while also meeting the production constraints. The standard model yields a higher profit ($31) than the deluxe model ($23). Given the constraints, producing 160 standard models and 80 deluxe models daily satisfies the minimum production requirements (at least 100 standard and at least 80 deluxe), does not exceed the maximum daily production limit of 240 phones, and maximizes profit by prioritizing the production of the more profitable standard model.

Question 8

Sketch the region R determined by the given constraints, and label its vertices. Find the maximum value of C on R.    
A)maximum of 20 at 
B)maximum of 24 at 
C)maximum of 0 at 
D)maximum of 22 at 
E)maximum of 18 at

Accepted Answer

The answer of Sketch the region R determined by the...

Question 9

Use the method of substitution to solve the system. 
A) 
B) 
C) 
D) 
E)no solution

Accepted Answer

The answer of Use the method of substitution to solve...

Question 10

Find a system of inequalities for the graph shown. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find a system of inequalities for the...

Question 11

Use matrices to solve the system. 
A) 
B) 
C) 
D)The system is dependent
E)No solution

Accepted Answer

The answer of Use matrices to solve the system. 
A)...

Question 12

Solve the system using the inverse method. 
A) 
B) 
C) 
D)The system is inconsistent.
E)The equations are dependent.

Accepted Answer

The answer of Solve the system using the inverse method....

Question 13

Use the method of substitution to solve the system. 
A)( - 4, -21 )
B)( - 4, -21 ), ( 9, 44 )
C)( - 4, -21 ), ( 8, 44 )
D)( 9, 44 )
E)no solution

Accepted Answer

The answer of Use the method of substitution to solve...

Question 14

Use matrices to solve the system. 
A) 
B) 
C) 
D)The equations are dependent
E)No solution

Accepted Answer

The answer of Use matrices to solve the system. 
A)...

Question 15

Solve the system  using the inverse method.
A) 
B) 
C) 
D)The system is inconsistent
E)The equations are dependent

Accepted Answer

The answer of Solve the system  using the inverse...

Question 16

A small firm manufactures bookshelves and desks for microcomputers. For each product it is necessary to use a table saw and a power router. To manufacture each bookshelf, the saw must be used for  hour and the router for 1 hour. A desk requires the use of each machine for 2 hours. The profits are $20 per bookshelf and $50 per desk. If the saw can be used for 8 hours per day and the router for 12 hours per day, how many bookshelves and desks should be manufactured each day to maximize the profit?
A)4 bookshelves and 2 desks
B)2 bookshelves and 2 desks
C)2 bookshelves and 4 desks
D)0 bookshelves and 4 desks
E)2 bookshelves and 0 desks

Accepted Answer

The answer of A small firm manufactures bookshelves and desks...

Question 17

Find the inverse of the matrix if it exists. 
A) 
B) 
C) 
D) 
E)Does not exist

Accepted Answer

The answer of Find the inverse of the matrix if...

Question 18

Find the inverse of the matrix if it exists. 
A) 
B) 
C) 
D) 
E)Does not exist

Accepted Answer

The answer of Find the inverse of the matrix if...

Question 19

Three average monthly low temperatures for Detroit are listed in the table. 
Let  correspond to January,  to February, . . . , and  to December. Determine a quadratic function  that interpolates the data - that is, determine the constants a, b, and c such that  , and  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Three average monthly low temperatures for Detroit...

Question 20

Use the method of substitution to solve the system. 
A)( 0, 2 )
B)( 4, 0 )
C)( 4, 0 ), ( 0, 2 )
D)( 4, 1 ), ( 0, 2 )
E)no solution

Accepted Answer

The answer of Use the method of substitution to solve...

Quiz 9: Systems of Equations and Inequalities

Use the method of substitution to solve the system.

Solve the system using the inverse method.

Solve the system.

Solve the system using the inverse method.

Find the inverse of the matrix if it exists.

Sketch the region R determined by the given constraints, and label its vertices. Find the maximum value of C on R.

Use the method of substitution to solve the system.

Find a system of inequalities for the graph shown.

Use matrices to solve the system.

Solve the system using the inverse method.

Use the method of substitution to solve the system.

Use matrices to solve the system.

Solve the system using the inverse method.

Find the inverse of the matrix if it exists.

Find the inverse of the matrix if it exists.

Three average monthly low temperatures for Detroit are listed in the table. Let correspond to January, to February, . . . , and to December. Determine a quadratic function that interpolates the data - that is, determine the constants a, b, and c such that , and .

Use the method of substitution to solve the system.