18.Formulate the situation as a system of two linear equations in two variables. Be sure to state clearly the meaning of yourx- andy-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$6,000or$12,000. If the partnership raised$522,000, then how many investors contributed$6,000and how many contributed$12,000?

x=$6,000investors

y =$12,000investors

19.Find the dimension of the matrix.

2 7

1 9

6 1

______________________

Find the values of the specified elements.

a_1,1=

a_3,2=

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.

R₁R₂on 5422

6323

22.Carry out the row operation on the matrix.

R₁R₂R₁on3452

5951

23.Carry out the row operation on the matrix.

1

5

R₂R₂on2342

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.)

104

019

(x,y)=

25.Express the situation as a system of two equations in two variables. Be sure to state clearly the meaning of yourx- andy-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$43,000to 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 contact152,000voters 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 parametert.)

1007

0103

0011

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

101 6

0105

0017

29.Use the given matrix to find the expression.

C=131

637 ;3C

535

3C=

30.Use the given matrices to find the expression.

A=511

519

727

C=883

216

134

; A+C

A+C=

31.Find the matrix product.

215 1

553 5

5

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

x₁+5x₂+4

x₃=4x₁+x₂+x₃=5

4x₁+2x₂+2x₃=2

33.Formulate the situation as a system of inequalities. (Letxrepresent the number of dinghies the company can manufacture andyrepresent 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)DinghyRowboatLabor Available

Metal Work23108

Painting2290

______________(labor for metal work)

______________(labor for painting)

Sketch the feasible region.

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

(x,y) =

(x,y) =

(x,y) =

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.)

MinimizeC=15x+60y

Subject to2x+ 5y20

x0,y0