question archive 1)Formulate the situation as a system of two linear equations in two variables

1)Formulate the situation as a system of two linear equations in two variables

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1)Formulate the situation as a system of two linear equations in two variables. Be sure to state clearly the meaning of your x- and y-variables. Solve the system by the elimination method. Be sure to state your final answer in terms of the original question.

 

A lawyer has found 60 investors for a limited partnership to purchase an inner-city apartment building, with each contributing either $6,000 or $12,000. If the partnership raised $522,000, then how many investors contributed $6,000 and how many contributed $12,000?

x =  $6,000 investors

y  =  $12,000 investors

 

19.Find the dimension of the matrix.

2   7

1   9

6   1

 

__________?____________

 

Find the values of the specified elements.

a1,1 =

a3,2 =

 

 

20.Find the augmented matrix representing the system of equations.

x + 5y = 6

7x + 3y = 15

 

 

21.arry out the row operation on the matrix.

R1 ↔ R2  on 5  4    22

6  3    23

 

22.Carry out the row operation on the matrix.

R1 − R2 → R1  on   3  4    52

5  9    51

 

23.Carry out the row operation on the matrix.

1

5

R2 → R2  on   2  −3    −42

0   5     100

 

24.Interpret the augmented matrix as the solution of a system of equations. (Enter your answers as a comma-separated list. If the system is inconsistent, enter INCONSISTENT. If the system is dependent, enter DEPENDENT.)

1  0    4

0  1    −9

 

(xy)=

 

25.Express the situation as a system of two equations in two variables. Be sure to state clearly the meaning of your x- and y-variables. Solve the system by row-reducing the corresponding augmented matrix. State your final answer in terms of the original question.

 

For the final days before the election, the campaign manager has a total of $43,000 to spend on TV and radio campaign advertisements. Each TV ad costs $3000 and is seen by 10,000 voters, while each radio ad costs $500 and is heard by 2000 voters. Ignoring repeated exposures to the same voter, how many TV and radio ads will contact 152,000 voters using the allocated funds?

x =  TV ads

y =  radio ads

 

26.Find the augmented matrix representing the system of equations.

x1 + x2 + x3 = 5

x1 + 5x2 + x3 = 3

x1 + 5x2 + 4x3 = 2

 

27.Interpret the row-reduced matrix as the solution of a system of equations. (Enter your answers as a comma-separated list. If the system is inconsistent, answer INCONSISTENT. If the system is dependent, parametrize the solutions in terms of the parameter t.)

1  0  0    7

0  1  0    3

0  0  1    −1

 

28.Use an appropriate row operation or sequence of row operations to find the equivalent row-reduced matrix.

1  0  1     6

0  1  0    5

0  0  1    7

 

29.Use the given matrix to find the expression.

C = 1  3  1

6  3  7 ;  3C

5  3  5

 

3C =

 

30.Use the given matrices to find the expression.

A = 5  1  1

5  1  9

7  2  7

 C = 8  8  3

2  1  6

1  3  4

;  A + C

 

A + C =

 

31.Find the matrix product.

2  1  5 1

5  5  3 −5

5

 

32.Rewrite the system of linear equations as a matrix equation AX = B.

x1 + 5x2 + 4

x3 = 4x1 + x2 + x3 = 5

4x1 + 2x2 + 2x3 = 2

 

33.Formulate the situation as a system of inequalities. (Let x represent the number of dinghies the company can manufacture and y represent the number of rowboats.)

A boat company manufactures aluminum dinghies and rowboats. The hours of metal work and painting needed for each are shown in the table, together with the hours of skilled labor available for each task. How many of each kind of boat can the company manufacture?

 

(hours)                 Dinghy    Rowboat      Labor Available

Metal Work          2                 3                   108

Painting                 2                 2                     90

 

______________(labor for metal work)  

______________(labor for painting)

 

Sketch the feasible region.

 

Find the vertices. (Order your answers from smallest to largest x, then from smallest to largest y.)(xy) =    

(xy) =    

(xy) =    

(xy) =    

 

 

34.Solve the linear programming problem by sketching the region and labeling the vertices, deciding whether a solution exists, and then finding it if it does exist. (If an answer does not exist, enter DNE.)

 

Minimize    C = 15x + 60y

Subject to    2x + 5y ≥ 20

x ≥ 0,  y ≥ 0

 

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