Question 1

Find the determinant of the matrix.

Accepted Answer

A) - 89,090 
B) - 1,425,432 
C) - 356,359 
D) 356,358 
E) - 356,358

Question 2

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  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 3

Use matrices to solve the system.

Accepted Answer

A)   
B)   
C)   
D) The system is inconsistent 
E) The equations are dependent

Question 4

Use matrices to solve the system.

Accepted Answer

A)   
B)   
C)   
D) The system is inconsistent 
E) The equations are dependent

Question 5

A manufacturer of tennis rackets makes a profit of $15 on each oversized racket and $10 on each standard racket. To meet dealer demand, daily production of standard rackets should be between 25 and 75, and production of oversized rackets should be between 8 and 27. To maintain high quality, the total number of rackets produced should not exceed 75 per day. How many of each type should be manufactured daily to maximize the profit?

Accepted Answer

A) 25 standard and 8 oversized 
B) 25 standard and 27 oversized 
C) 27 standard and 48 oversized 
D) 48 standard and 27 oversized 
E) 48 standard and 8 oversized

Question 6

Use Cramer's rule, whenever possible, to solve the system.

Accepted Answer

A)   
B)   
C)   
D) The equations are dependent. 
E) The system is inconsistent.

Question 7

Solve the system.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 8

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?

Accepted Answer

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

Question 9

Solve the system  using the inverse method.

Accepted Answer

A)   
B)   
C)   
D) The system is inconsistent 
E) The equations are dependent

Question 10

Find the inverse of the matrix if it exists.

Accepted Answer

A)   
B)   
C)   
D)   
E) Does not exist

Question 11

Use the method of substitution to solve the system.

Accepted Answer

A) ( - 1, -12 ), ( 8, 68 ) 
B) ( 9, 68 ) 
C) ( - 1, -12 ) 
D) ( - 1, -12 ), ( 9, 68 ) 
E) no solution

Question 12

Find the values of b such that the system  has no solution.

Accepted Answer

A)   
B)   
C)   
D)   
E) no solution

Question 13

Find a system of inequalities for the graph shown.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 14

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?

Accepted Answer

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

Question 15

Find the inverse of the matrix if it exists.

Accepted Answer

A)   
B)   
C)   
D)   
E) Does not exist

Question 16

Find the inverse of the matrix if it exists.

Accepted Answer

A)   
B)   
C)   
D)   
E) Does not exist

Question 17

Find the maximum and minimum values of the objective function  on the region in the figure.

Accepted Answer

A) The maximum is  at
 ,
The minimum is
 at
 . 
B) The maximum is  at
 ,
The minimum is
 at
 . 
C) The maximum is  at
 ,
The minimum is
 at
 . 
D) The maximum is  at
 ,
The minimum is
 at
 . 
E) The maximum is  at
 ,
The minimum is
 at
 .

Question 18

Sketch the graph of the inequality.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 19

Solve the system  using the inverse method.

Accepted Answer

A)   
B)   
C)   
D) The system is inconsistent 
E) The equations are dependent

Question 20

A manufacturer of tennis rackets makes a profit of $14 on each oversized racket and $8 on each standard racket. To meet dealer demand, daily production of standard rackets should be between 25 and 77, and production of oversized rackets should be between 10 and 30. To maintain high quality, the total number of rackets produced should not exceed 77 per day. How many of each type should be manufactured daily to maximize the profit?

Accepted Answer

A) 25 standard and 10 oversized 
B) 30 standard and 47 oversized 
C) 25 standard and 30 oversized 
D) 47 standard and 10 oversized 
E) 47 standard and 30 oversized

Exam 9: Systems of Equations and Inequalities

Find the determinant of the matrix.

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 matrices to solve the system.

Use matrices to solve the system.

Use Cramer's rule, whenever possible, to solve the system.

Solve the system.

Solve the system using the inverse method.

Find the inverse of the matrix if it exists.

Use the method of substitution to solve the system.

Find the values of b such that the system has no solution.

Find a system of inequalities for the graph shown.

Find the inverse of the matrix if it exists.

Find the inverse of the matrix if it exists.

Find the maximum and minimum values of the objective function on the region in the figure.

Sketch the graph of the inequality.

Solve the system using the inverse method.