BUSINESS MATH EXAM #3 BOOK
QUESTIONS WITH CORRECT ANSWERS
5.2.57. Harv, the owner of Harv's Meats, knows that he must buy a new deboner
machine in 4 years. The machine costs $12,000. In order to accumulate enough money
to pay for the machine, Harv decides to deposits a sum of money at the end of each 6
months in an account paying 6% compounded semiannually. How much should each
payment be? - ANSWER-$1349.48
5.2.59. Taylor Larson is paid on the first of the month and $80 is automatically deducted
from her pay and deposited in a savings account. If the account pays 2.5% interest
compounded monthly, how much will be in the account after 3 years and 9 months? -
ANSWER-$3777.89
5.2.63. To save for retirement, Karla Harby put $300 each month into an ordinary
annuity for 20 years. Interest was compounded monthly. At the end of the 20 years, the
annuity was worth $147,126. What annual interest rate did she receive? - ANSWER-
6.5%
5.3.37. David Kurzawa buys a car costing $14,000. He agrees to make payments at the
end of each monthly period for 4 years. He pays 7% interest, compounded monthly.
(a) What is the amount of each payment?
(b) Find the total amount of interest David will pay. - ANSWER-(a) $335.25
(b) $2092
5.3.47a. In 1995, Oseola McCarty donated $150,000 to the University of Southern
Mississippi to establish a scholarship fund. What is unusual about her is that the entire
amount came from what she was able to save each month from her work as a washer
woman, a job she began in 1916 at the age of 8, when she dropped out of school.
(a) How much would Ms. McCarty have to put into her savings account at the end of
every 3 months to accumulate $150,000 over 79 years? Assume she received an
interest rate of 5.25% compounded quarterly. - ANSWER-(a) $32.49
5.3.49c. Jason Hoffa buys a house for $285,000. He pays $60,000 down and takes out
a mortgage at 6.5% on the balance. Find his monthly payment and the total amount of
interest he will pay if the length of the mortgage is
(c) 25 years - ANSWER-(c) $1519.22; $230,766.00
, 4.1.5. For Exercises 5-8, (a) determine the number of slack variables needed, (b) name
them, and (c) use slack variables to convert each constraint into a linear equation.
Maximize z = 5x1 + 7x2
subject to: 2x1 + 3x2 =< 15
4x1 + 5x2 =< 35
x1 + 6x2 =< 20
with x1 => 0, x2 => 0 - ANSWER-(a) 3
(b) s1, s2, s3
(c) 2x1 + 3x2 + s1 = 15; 4x1 + 5x2 + s2 = 35; x1 + 6x2 + s3 = 20
4.1.7. For Exercises 5-8, (a) determine the number of slack variables needed, (b) name
them, and (c) use slack variables to convert each constraint into a linear equation.
Maximize z = 12x1 + 15x2 + 10x3
subject to: 7x1 + 6x2 + 8x3 =< 118
4x1 + 5x2 + 10x3 =< 220
with x1 => 0, x2 => 0, x3 => 0 - ANSWER-(a) 2
(b) s1, s2
(c) 7x1 + 6x2 + 8x3 + s1 = 118; 4x1 + 5x2 + 10x3 + s2 = 220
4.1.27. The authors of a best-selling textbook in finite mathematics are told that, for the
next edition of their book, each simple figure would cost the project $20, each figure
with additions would cost $35, and each computer-drawn sketch would cost $60. They
are limited to 400 figures, for which they are allowed to spend up to $2200. The number
of computer-drawn sketches must be no more than the number of the other two types
combined, and there must be at least twice as many simple figures as there are figures
with additions. If each simple figure increases the royalties by $95, each figure with
additions increases royalties by $200, and each computer-drawn figure increases
royalties by $325, how many of each type of figure should be included to maximize
royalties, assuming that all art costs are borne by the publisher? - ANSWER-If x1 is the
number of simple figures, x2 is the number of figures with additions, and x3 is the
number of computer-drawn sketches, find x1 => 0, x2 => 0, and x3 => 0 such that 20x1
+ 35x2 + 60x3 =< 2200, x1 + x2 + x3 =< 400, x3 =< x1 + x2, x1 => 2x2, and z = 95x1 +
200x2 + 325x3 is maximized; 20x1 + 35x2 + 60x3 + s1 = 2200, x1 + x2 + x3 + s2 = 400,
-x1 - x2 + x3 + s3 = 0, -x1 + 2x2 + s4 = 0.
4.1.29. A charity wants to produce as many jackets as possible before winter starts for
people living in a refugee camp. They have 3 styles of jackets they can produce. The
first requires 6 sq ft of nylon and 2 sq ft of fleece. The second requires 4 sq ft of nylon
and 3 sq ft of fleece, while the third requires 3 sq ft of nylon and 5 sq ft of fleece. The
costs to produce each of the three styles of jackets are $20, $18, and $17, respectively.
QUESTIONS WITH CORRECT ANSWERS
5.2.57. Harv, the owner of Harv's Meats, knows that he must buy a new deboner
machine in 4 years. The machine costs $12,000. In order to accumulate enough money
to pay for the machine, Harv decides to deposits a sum of money at the end of each 6
months in an account paying 6% compounded semiannually. How much should each
payment be? - ANSWER-$1349.48
5.2.59. Taylor Larson is paid on the first of the month and $80 is automatically deducted
from her pay and deposited in a savings account. If the account pays 2.5% interest
compounded monthly, how much will be in the account after 3 years and 9 months? -
ANSWER-$3777.89
5.2.63. To save for retirement, Karla Harby put $300 each month into an ordinary
annuity for 20 years. Interest was compounded monthly. At the end of the 20 years, the
annuity was worth $147,126. What annual interest rate did she receive? - ANSWER-
6.5%
5.3.37. David Kurzawa buys a car costing $14,000. He agrees to make payments at the
end of each monthly period for 4 years. He pays 7% interest, compounded monthly.
(a) What is the amount of each payment?
(b) Find the total amount of interest David will pay. - ANSWER-(a) $335.25
(b) $2092
5.3.47a. In 1995, Oseola McCarty donated $150,000 to the University of Southern
Mississippi to establish a scholarship fund. What is unusual about her is that the entire
amount came from what she was able to save each month from her work as a washer
woman, a job she began in 1916 at the age of 8, when she dropped out of school.
(a) How much would Ms. McCarty have to put into her savings account at the end of
every 3 months to accumulate $150,000 over 79 years? Assume she received an
interest rate of 5.25% compounded quarterly. - ANSWER-(a) $32.49
5.3.49c. Jason Hoffa buys a house for $285,000. He pays $60,000 down and takes out
a mortgage at 6.5% on the balance. Find his monthly payment and the total amount of
interest he will pay if the length of the mortgage is
(c) 25 years - ANSWER-(c) $1519.22; $230,766.00
, 4.1.5. For Exercises 5-8, (a) determine the number of slack variables needed, (b) name
them, and (c) use slack variables to convert each constraint into a linear equation.
Maximize z = 5x1 + 7x2
subject to: 2x1 + 3x2 =< 15
4x1 + 5x2 =< 35
x1 + 6x2 =< 20
with x1 => 0, x2 => 0 - ANSWER-(a) 3
(b) s1, s2, s3
(c) 2x1 + 3x2 + s1 = 15; 4x1 + 5x2 + s2 = 35; x1 + 6x2 + s3 = 20
4.1.7. For Exercises 5-8, (a) determine the number of slack variables needed, (b) name
them, and (c) use slack variables to convert each constraint into a linear equation.
Maximize z = 12x1 + 15x2 + 10x3
subject to: 7x1 + 6x2 + 8x3 =< 118
4x1 + 5x2 + 10x3 =< 220
with x1 => 0, x2 => 0, x3 => 0 - ANSWER-(a) 2
(b) s1, s2
(c) 7x1 + 6x2 + 8x3 + s1 = 118; 4x1 + 5x2 + 10x3 + s2 = 220
4.1.27. The authors of a best-selling textbook in finite mathematics are told that, for the
next edition of their book, each simple figure would cost the project $20, each figure
with additions would cost $35, and each computer-drawn sketch would cost $60. They
are limited to 400 figures, for which they are allowed to spend up to $2200. The number
of computer-drawn sketches must be no more than the number of the other two types
combined, and there must be at least twice as many simple figures as there are figures
with additions. If each simple figure increases the royalties by $95, each figure with
additions increases royalties by $200, and each computer-drawn figure increases
royalties by $325, how many of each type of figure should be included to maximize
royalties, assuming that all art costs are borne by the publisher? - ANSWER-If x1 is the
number of simple figures, x2 is the number of figures with additions, and x3 is the
number of computer-drawn sketches, find x1 => 0, x2 => 0, and x3 => 0 such that 20x1
+ 35x2 + 60x3 =< 2200, x1 + x2 + x3 =< 400, x3 =< x1 + x2, x1 => 2x2, and z = 95x1 +
200x2 + 325x3 is maximized; 20x1 + 35x2 + 60x3 + s1 = 2200, x1 + x2 + x3 + s2 = 400,
-x1 - x2 + x3 + s3 = 0, -x1 + 2x2 + s4 = 0.
4.1.29. A charity wants to produce as many jackets as possible before winter starts for
people living in a refugee camp. They have 3 styles of jackets they can produce. The
first requires 6 sq ft of nylon and 2 sq ft of fleece. The second requires 4 sq ft of nylon
and 3 sq ft of fleece, while the third requires 3 sq ft of nylon and 5 sq ft of fleece. The
costs to produce each of the three styles of jackets are $20, $18, and $17, respectively.
