LINEAR PROGRAMMING

1
LINEAR PROGRAMMING

• WORD PROBLEMS WITH ANSWERS

2
1. Mary works selling cards over the telephone.
She sells two types of cards, birthday cards and
holiday cards. Mary makes 2.00 for each box of
birthday cards she sells, and she makes 2.50 for
each box of holiday cards she sells. She can work
no more than 10 hours per week. It takes her an
average of 15 minutes to sell one box of birthday
cards and an average of 20 minutes to sell one
box of holiday cards. If she can sell no more
than 35 boxes of cards in total, how many boxes
of each type should she sell to make the most
money? (Hint remember that an hour contains 60
minutes!)
x birthday cards y holiday cards
P 2x 2.50y
Vertices (0, 0) 0.00 (0, 30)
75.00 (20, 15) 77.50 (35, 0) 70.00
Answer 20 birthday cards and 15 holiday cards
max profit 77.50
3
2. Your factory makes fruit filled breakfast
bars and granola bars. For each case of breakfast
bars, you make a 40 profit. For each case of
granola bars, you make a 55 profit. It takes 2
machine hours to make a case of breakfast bars
and 5 hours of labor. It takes 6 machine hours
and 4 labor hours to make s case of granola bars.
You have a maximum of 150 machine hours and 160
labor hours available. How many cases of each
product should you produce in order to maximize
profit?
x breakfast bar y granola bar
P 40x 55y
Vertices (0, 0) 0.00 (0, 25)
1375.00 (15,20) 1700.00 (32, 0) 1280.00
Answer approximately 15 cases of breakfast bars
and 20 cases of granola bars max profit -
1700.00
4
3. An oil refinery has a maximum production of
2,000 barrels of oil per day. It produces two
types of petroleum products gasoline and heating
oil. The government requires that the refinery
produce at least 300 barrels of heating oil per
day. If the profit is 3.00 per barrel of
gasoline and 2 a barrel for heating oil, how
much of each petroleum product should the oil
refinery produce per day to maximize profit? What
is the maximum profit per day?
x gasoline y heating
P 3x 2y
Vertices (0, 300) 600.00 (0, 2000)
4000.00 (1700, 300) 5700.00
Answer 1700 barrels of gasoline and 300 barrels
of heating max profit - 5700.00
5
4. A Virginia Beach farmer has 480 acres of
land on which to grow either corn or soybeans. He
figures he has 800 hours of labor available
during the crucial summer season. The farmer can
expect a profit of 40 per acre on corn and 30
per acre on soybeans. He knows that corn requires
2 hours per acre to raise, and soybeans require 1
hour per acre to raise. How many acres of each
should he plant to maximize profit? What is his
maximum profit?
x acre of corn y acre of soybeans
P 40x 30y
Vertices (0, 0) 0.00 (0, 480)
14400.00 (400, 0) 16000.00 (320, 160)
17600.00
Answer 320 acres of corn and 160 acres of
soybeans max profit - 17,600.00
6
5. Brad owns a news stand that has room for 100
newspapers per day. In his town, there are two
papers, The Journal and The Globe. Every day,
Brad sells 20 Journals and 25 Globes to customers
with subscriptions. If Brad makes 0.05 for every
Journal sold and 0.10 for each Globe sold, how
many Journals and how many Globes should he put
on his stand to make the most money?
x of The Journal y of The Globe
P .05x .10y
Vertices (20, 25) 3.50 (20, 80)
9.00 (75, 25) 6.25
Answer 20 The Journal and 80 The Globe max
profit - 9.00
7
6. Your club plans to raise money by selling two
sizes of fruit baskets. The Plan is to buy small
baskets for 10 and sell them for 16, then buy
large baskets for 15 and sell them for 25. The
club president estimates that you will not sell
more than 100 baskets. Your club can afford to
spend up to 1,200 to but baskets. Find the
number of small and large fruit baskets you
should buy in order to maximize profit.
x of small fruit baskets y of large fruit
baskets
P 6x 10y
Vertices (0, 0) 0.00 (0, 80)
800.00 (100, 0) 600.00 (60, 40) 760.00
Answer 0 small fruit baskets and 80 large fruit
baskets max profit - 800.00
8
LINEAR PROGRAMMING

• ACTIVITY SHEET
• WORD PROBLEMS WITH ANSWERS

9
1. The Buds-R-Us Florist has to order roses and
carnations for Valentines Day. Roses cost the
florist 20 per dozen and carnation cost 5 per
dozen. The profit on roses is 20 per dozen and
on carnations it is 8 per dozen. The florist can
spend at most 450 on flowers and must order at
least 20 dozen carnations, but the florist can
order no more than 60 dozen flowers. How many of
each kind should he order in order to maximize
the profit?
x dozens of roses y dozens of carnations
P 20x 8y
Vertices (10, 50) 600.00 (17, 20)
500.00 (40, 20) 960.00
Answer 40 dozens of roses and 20 dozens of
carnations max profit - 960.00
10
2. U. N. Scrupulous, a noted businessman in
town, always uses both newspaper and radio
advertising each month. It is estimated that each
newspaper ad reaches 8,000 people and that each
radio ad reaches 15,000 people. Each newspaper ad
costs 50 and each radio ad costs 100. The
business can spend no more than 1000 for
advertising per month. The newspaper requires at
least 4 ads be purchased each month and the radio
requires that at least 5 ads be purchased each
month. What combination of newspaper and radio
ads should old Scrupe purchase in order to
reach the maximum number of people?
x newspaper ad y radio ad
P 8000x 15000y
Vertices (4, 8) 152,000 people (4, 5)
107,000 people (10, 5) 155,000 people
Answer 10 newspaper ads and 5 radio ads max
people reached 155,000
11
3. The campus store sells stadium cushions and
caps. The cushions cost 1.90 the caps cost
2.25. They sell the cushions for 5.00 and the
caps for 6.00. They can obtain no more than 100
cushions and 75 caps per week. To meet the
demands, they have to sell a total of at least
120 of the two items together. They cannot
package more than 150 per week. How many of each
should they sell to maximize profit?
x cushions y caps
P 3.1x 3.75y
Vertices (45, 75) 420.75 (75, 75)
513.75 (100, 20) 385.00 (100, 50) 497.50
Answer 75 cushions and 75 caps max profit -
513.75