MATH 1324 Midterm Exam 2015

Midterm MATH1324

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find an equation in slope intercept form (where possible) for the line.

1) Through (3, 1), m = -3

A) y = 3x + 10 B) y = 3x - 8 C) y = -3x + 10 D) y = -3x - 8

1)

Solve the problem.

2) After two years on the job, an engineer's salary was $60,000. After seven years on the job, her

salary was $72,500. Let y represent her salary after x years on the job. Assuming that the change in

her salary over time can be approximated by a straight line, give an equation for this line in the

form y = mx + b.

A) y = 2500x + 55,000 B) y = 12,500x + 60,000

C) y = 12,500x + 35,000 D) y = 2500x + 60,000

2)

3) Let the demand and supply functions be represented by D(p) and S(p), where p is the price in

dollars. Find the equilibrium price and equilibrium quantity for the given functions.

D(p) = 115,620 - 250p

S(p) = 570p

A) $202; 65,120 B) $320; 80,370 C) $141; 80,370 D) $320; 35,620

3)

4) A book publisher found that the cost to produce 1000 calculus textbooks is $25,200, while the cost

to produce 2000 calculus textbooks is $52,000. Assume that the cost C(x) is a linear function of x,

the number of textbooks produced. What is the marginal cost of a calculus textbook?

A) $2.68 B) $26,800.00 C) $26.80 D) $0.03

4)

Find the equation of the least squares line.

5) The paired data below consist of the test scores of 6 randomly selected students and the number of

hours they studied for the test.

Hours (x) 5 10 4 6 10 9

Score (y) 64 86 69 86 59 87

A) y = 33.7 - 2.14x B) y = -67.3 + 1.07x

C) y = 33.7 + 2.14x D) y = 67.3 + 1.07x

5)

Use the echelon method to solve the system of two equations in two unknowns.

6) x - 3y = 25

-2x - 4y = 20

A) (3, -6) B) (-4, -6) C) (4, -7) D) No solution

6)

Solve the problem.

7) There were 32,000 people at a ball game in Los Angeles. The day's receipts were $236,000. How

many people paid $13 for reserved seats and how many paid $ 4 for general admission?

A) 27,000 paid $13; 5000 paid $4. B) 12,000 paid $13; 20,000 paid $4.

C) 5000 paid $13; 27,000 paid $4. D) 20,000 paid $13; 12,000 paid $4.

7)

1

Use the Gauss Jordan method to solve the system of equations.

8) x + y + z = -1

x - y + 3z = -7

4x + y + z = -7

A) (-1, -2, 2) B) (-2, 2, -1) C) (-1, 2, -2) D) No solution

8)

Perform the indicated operation, where possible.

9) 4x + 3y 2x + 10y

3x - 10y 9x - 2y

+

10x + 10y -7x

10y - 9x -7x + 8y

A) 14x + 13y -5x + 10y

12x 2x + 10y

B) -6x - 7y 9 + 10y

12x 16x + 6y

C) 14x + 13y -5x + 10y

-6x 2x + 6y

D) 14x + 13y -5x + 10y

13x - 19y 2x + 6y

9)

Find the matrix product, if possible.

10) -1 3

4 2

-2 0

-1 1

A) 3 -1

2 -10

B) -1 3

-10 2

C) 2 0

-4 2

D) 2 -6

-3 -1

10)

Find the inverse, if it exists, for the matrix.

11) 2 6

-1 -2

A)

1

2

1

- 1 - 3

B)

- 1 3

-

1

2

1

C)

1 - 3

1

2

- 1

D)

- 1 - 3

1

2

1

11)

Solve the system of equations by using the inverse of the coefficient matrix if it exists and by the echelon method if the

inverse doesn't exist.

12) -2x + 6y = 6

3x + 2y = 13

A) (3, 2) B) (-3, -2) C) (2, 3) D) (-2, -3)

12)

Solve the problem.

13) A company makes three chocolate candies: cherry, almond, and raisin. Matrix A gives the amount

of ingredients in one batch. Matrix B gives the costs of ingredients from suppliers X and Y. What is

the cost of 100 batches of each candy using ingredients from supplier X?

A =

sugar

4

5

3

choc

6

3

3

milk

1

1

1

cherry

almond

raisin

B =

X

3

3

2

Y

2

4

2

sugar

choc

milk

A) $6600 B) $3300 C) $7800 D) $4800

13)

Graph the feasible region for the system of inequalities.

2

14) 2x + y ? 3

x - y ? 3

-10 -5 5 10 x

y

10

5

-5

-10

-10 -5 5 10 x

y

10

5

-5

-10

A)

-10 -5 5 10 x

y

10

5

-5

-10

-10 -5 5 10 x

y

10

5

-5

-10

B)

-10 -5 5 10 x

y

10

5

-5

-10

-10 -5 5 10 x

y

10

5

-5

-10

C)

-10 -5 5 10 x

y

10

5

-5

-10

-10 -5 5 10 x

y

10

5

-5

-10

D)

-10 -5 5 10 x

y

10

5

-5

-10

-10 -5 5 10 x

y

10

5

-5

-10

14)

3

Write the system of inequalities that describes the possible solutions to the problem.

15) A manufacturer of wooden chairs and tables must decide in advance how many of each item will

be made in a given week. Use the table to find the system of inequalities that describes the

manufacturer's weekly production.

Use x for the number of chairs and y for the number of tables made per week. The number of

work-hours available for construction and finishing is fixed.

Hours

per

chair

Hours

per

table

Total

hours

available

Construction 2 3 36

Finishing 2 2 28

A) 2x + 3y ? 28

2x + 2y ? 36

x ? 0

y ? 0

B) 2x + 3y ? 36

2x + 2y ? 28

x ? 0

y ? 0

C) 2x + 3y ? 28

2x + 2y ? 36

x ? 0

y ? 0

D) 2x + 3y ? 36

2x + 2y ? 28

x ? 0

y ? 0

15)

Use the indicated region of feasible solutions to find the maximum and minimum values of the given objective

function.

16) z = 11x + 3y

x

y

(10, 5)

(10, 0)

(0, 5)

(0, 3)

(2, 0) x

y

(10, 5)

(10, 0)

(0, 5)

(0, 3)

(2, 0)

A) Maximum of 125; minimum of 110 B) Maximum of 110; minimum of 9

C) Maximum of 125; minimum of 9 D) Maximum of 15; minimum of 9

16)

4

Use graphical methods to solve the linear programming problem.

17) Maximize z = 6x + 7y

subject to: 2x + 3y ? 12

2x + y ? 8

x ? 0

y ? 0

-10 10 x

y

10

-10

A) Maximum of 24 when x = 4 and y = 0 B) Maximum of 32 when x = 3 and y = 2

C) Maximum of 32 when x = 2 and y = 3 D) Maximum of 52 when x = 4 and y = 4

17)

Express the given situation as a linear inequality.

18) Product A requires 4 hr on machine M, while product B needs 3 hr on the same machine. The

machine is available for at most 48 hr per week. Let x be the number of product A made and y be

the number of product B.

A) 48(x + y) ? 7 B) x + y ? 48 C) 7(x + y) ? 48 D) 4x + 3y ? 48

18)

Solve the problem.

19) A company manufactures two ballpoint pens, silver and gold. The silver requires 3 min in a

grinder and 4 min in a bonder. The gold requires 3 min in a grinder and 8 min in a bonder. The

grinder can be run no more than 87 hours per week and the bonder no more than 51 hours per

week. The company makes a $ 8 profit on each silver pen sold and $12 on each gold. How many of

each type should be made each week to maximize profits?

A) Silver pens: 0

Gold pens: 381

B) Silver pens: 1

Gold pens: 382

C) Silver pens: 1359

Gold pens: 381

D) Silver pens: 382

Gold pens: 1359

19)

20) If $3500 earned simple interest of $153.13 in 7 months, what was the simple interest rate?

A) 6.5% B) 8.5% C) 7.5% D) 9.5%

20)

Find the compound amount for the deposit. Round to the nearest cent.

21) $9000 at 8% compounded annually for 5 years

A) $12,600.00 B) $11,880.00 C) $12,244.40 D) $13,223.95

21)

Find the future value of the ordinary annuity. Interest is compounded annually, unless otherwise indicated.

22) R = $100, i = 0.06, n = 9

A) $265.64 B) $989.75 C) $1149.13 D) $2815.80

22)

5

Solve the problem. Round to the nearest cent.

23) If Bob deposits $5000 at the end of each year for 2 years in an account paying 6% interest

compounded annually, find the final amount he will have on deposit.

A) $5000.00 B) $15,918.00 C) $5300.00 D) $10,300.00

23)

Find the present value of the ordinary annuity.

24) Payments of $470 made annually for 13 years at 6% compounded annually

A) $4368.65 B) $3940.39 C) $4159.27 D) $4160.76

24)

Solve the problem.

25) Tasha borrowed $14,000 to purchase a new car at an annual interest rate of 8.9%. She is to pay it

back in equal monthly payments over a 4 year period. What is her monthly payment?

A) $405.77 B) $103.83 C) $25.96 D) $347.73

25)