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
workhours 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)

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Solution: MATH 1324 Midterm Exam 2015 Solution