2. Linear Programming
- Is one of the main applications of
mathematics used in business and
the social sciences.
- Is used to find the minimum cost,
maximum profit, the maximum
amount of learning that can take
place under given conditions, and
so on.
3. Linear Programming
- Was developed by George
Dantzig in 1947, while working on
the problem of allocating supplies
for Air Force troops during the
World War II, in a way that
minimized cost
8. 7. Test all corner points in
your objective quantity (to
determine the max/min).
8. Answer the question in
a sentence.
9. Example:
1. You are taking a test in which each
item of type A is worth 10 points and
items of type B is worth 15 points. It
takes 3 minutes for each item of type A
and 6 minutes for each item of type B.
The total time allowed is 60 minutes, and
you may not answer more than 16
questions. Assuming all your answers
are correct, how many items of each type
should you answer in order to get the
best score?
10. Solution:
Step 1: Read and reread the
question.
Step 2:
Let x – be the number of type
A questions.
Let y – be the number of type
B questions.
11. Step 3:
Objective Quantity: (to be maximized)
10x + 15y
Step 4:
Constraints:
3x + 6y ≤ 60 (allotted time)
x + y ≤ 16 ( number of items to
answer)
13. Step 8:
Therefore, in order for
you to get the best score,
you must answer 12 type
A items and 4 type B
items.
14. Example 2:
A farmer has 3216 square meter-
farm where he raises chickens and
goats. Chickens require 2 sq. m while
goats need 24 sq. m each. The per-
head profit on chickens and goats are
Php11 and Php130, respectively. If he
cannot tend to more than 1500 chickens
or 120 goats, how many of each type
should he have in order to make the
largest profit?
15. Solution:
Step 1: Read and reread the
question.
Step 2:
Let x – be the number of
chickens.
Let y – be the number of goats.
16. Step 3:
Objective Quantity: (to be maximized)
11x + 130y
Step 4:
Constraints:
2x + 24y ≤ 3216 (area of the farm)
x ≤ 1500 (chickens)
y ≤ 120
18. Step 8:
Therefore, in order to
make the largest profit,
the farmer should have
1500 chickens and 9
goats.
19. ACTIVITY
Mechanics:
1. The class will be divided into 6 groups. Each member will
be assigned with a specific number from 2-8 which
corresponds the steps to be answered.
2. The question will be shown on the powerpoint presentation.
3. Each group will do the peer-teaching activity for 10 minutes.
They must discuss their answers silently and cooperatively.
4. Assigned members will write their answers on the manila
paper. Answers to be written will start with Step 2. Persons
assigned for Step 5 must have their graphs ready to be
posted.
5. There will be an allotted time for each step depending on
the level of difficulty.
6. The first group with the correct and accurate answers will
be declared as winner.
20. A snack bar cooks and sells hamburgers
and hotdogs during football games. To stay
in business, it must sell at least 10
hamburgers but can not cook more than 40.
it must also sell at least 30 hotdogs but
cannot cook more than 70. It cannot cook
more than 90 sandwiches all together. The
profit on a hamburger is $ 0.33 and $ 0.21 on
a hotdog. How many of each kind of sandwich
should the stand sell to make the maximum
profit?
