Practice
1. A scholarship administrator is using a $500,000 endowment to purchase two bonds. A corporate bond pays 8% interest per year and a safer treasury bond pays 5 ¼ % interest per year. If he needs at least $30,000 annual interest payments, what is the least he can spend on the corporate bond?
2. Kelly
sells corn dogs at a state fair. Booth rental and equipment rental total $200
per day. Each corn dog costs 35 cents to make and sells for $2. How many corn
dogs should she sell in order to have a daily profit of at least $460?
3. The
owner of a snow cone stand pays $200 per month to rent his equipment and $400
per month for a stall in a flea market. Each snow cone costs 25 cents to make
and sells for $1.50. How many snow cones does he need to sell in order to make
a profit?
4. A
tee-shirt stand can sell a certain sports tee shirt for $18. Each shirt costs
$8 in materials and labor. Monthly fixed costs are $1500. How many tee shirts
must be sold to guarantee a monthly profit of at least $3500?
5. A
car rental company rents a certain car for $40 per day with unlimited mileage
or $24 per day plus 80 cents per mile. What is the most a customer can drive
the car per day for the $24 option to cost no more than the unlimited mileage
option?
6. An
internet service provider offers two plans. One plan costs $25 per month and
allows unlimited internet access. The other plan costs $12 per month and allows
50 free hours plus 65 cents for each additional hour. How many hours per month
would a customer need to use in order for the unlimited access plan be less
expensive than the other plan?
7. Sharon
can purchase a pair of ice skates for $60. It costs her $3 to rent a pair each
time she goes to the rink. How many times would she need to use the skates to
make purchasing them more attractive than renting them?
8. The
James family has $210 budgeted each month for electricity. They have a monthly
base charge of $28 plus 7 cents per kilowatthour. How many kilowatt-hours can
they use each month to stay within their budget?
9. A
warehouse store charges an annual fee of $40 to shop there. A shopper without
paying this fee can still shop there if he pays a 5% buyer’s premium on his
purchases. How much would a shopper need to spend at the store to make paying
the annual $40 fee at least as attractive as paying the 5% buyer’s premium?
10. A sales
clerk at an electronics store is given the option for her salary to be changed
from a straight annual salary of $25,000 to an annual base salary of $15,000
plus an 8% commission on sales. What would her annual sales level need to be in
order for this option to be at least as attractive as the straight salary
option?
Solutions
1. Let
x = amount invested in the corporate bond
500,000
– x = amount invested in the treasury bond
0.08x
= annual interest from the corporate bond
0.0525(500,000
– x) = annual interest from the treasury bond
Corporate
bond interest + Treasury bond interest ≥ 30,000
The administrator should invest at least $136,363.64 in the corporate bond
in order to receive at least $30,000 per year in interest payments.
2. Let
x = number of corn dogs sold per day
2x
= revenue
200
+ 0.35x = overhead costs + production costs = total cost
Kelly needs to sell at least 400 corn dogs in order for her daily profit
to be at least $460.
3. Let
x = number of snow cones sold per month
1.50x
= revenue
600
+ 0.25x = overhead costs + production costs = total cost
The owner should sell more than 480 snow cones per month to make a
profit.
4. Let
x = number of tee shirts sold per month
18x
= revenue
1500
+ 8x = overhead costs + production costs = total cost
At least 500 tee shirts would need to be sold each month to make a monthly
profit of at least $3500.
5. Let
x = number of daily miles
The
$24 option costs 24 + 0.80x per day.
The most a customer could drive is 20 miles per day in order for the $24
plan to cost no more than the $40 plan.
6. The
first 50 hours are free under the $12 plan, so let x represent the number of
hours used beyond 50 hours. Each hour beyond 50 costs 0.65x.
A family would need to use more than 20 hours per month beyond 50 hours
(or more than 70 hours per month) in order for the unlimited plan to cost less
than the limited hour plan.
7. Let
x = number of times Sharon uses her skates
The
cost to rent skates is 3x.
Sharon would need to use her skates more than 20 times to justify purchasing
them instead of renting them.
8. Let
x = number of kilowatt-hours used per month 28 + 0.07x = monthly bill
The James family can use no more than 2600 kilowatt-hours per month in
order to keep their electricity costs within their budget.
9. Let
x = amount spent at the store annually 0.05x = extra 5% purchase charge per
year.
A shopper would need to spend at least $800 per year to justify the $40
annual fee.
10. Let
x = annual sales level
0.08x
= annual commission
15,000
+ 0.08x = annual salary plus commission
The
sales clerk would need an annual sales level of $125,000 or more in order for
the salary plus commission option to be at least as attractive as the straight
salary option.
“Sumber Informasi”
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