how we use linear programming to solve questions

2. MATHS PROJECT

3. TOPIC

4. What Is Linear Programming?
Linear programming also called as linear
optimization is a mathematical technique
to achieve the best outcome such as
maximum profit or lowest cost.

5. Methods To Solve
Simplex method
Graphical representation

6. Example Question
O Maximize 𝑃 = 12𝑥 + 14𝑦
Subject to: 3𝑥 + 3𝑦 ≤ 8
4𝑦 + 2𝑥 ≤ 8 availabilities
constraints

7. Solution
Standard form;
3𝑥 + 3𝑦 = 8
4𝑦 + 2𝑥 = 8 (2)
(1)
Put y=0
3x+3(0)=8
3x=8
x=8/3=2.6
𝟐. 𝟔, 𝟎
In eq (1)
Put x=0
3(0)+3y=8
3y=8
y=8/3=2.6
𝟎, 𝟐. 𝟔

8. In eq (2)
Put x=0
4y+2(0)=8
4y=8
y=8/4
y=2
𝟎, 𝟐
Put y=0
4(0)+2x=8
2x=8
x=8/2
x=4
𝟒, 𝟎

9. So these are the values of x and y respectively.
We will represent x values on the x-axis and y values
on the y-axis.
𝟎, 𝟐. 𝟔
𝟐. 𝟔, 𝟎
𝟎, 𝟐
𝟒, 𝟎

10. 1
2
3
4
5
y-axis
x-axis
1 2 3 4 5 6
6
B (1.3,1.5)
A (0,2)
C (2.6,0)
Remember
When constraints are
less than availabilities
then the inner area to
the feasible points will
be shaded and vice
versa.
The shaded area is called feasible region.
The points A,B & C are called corner or feasible points.

11. For optimum solution we will put the values of points
A,B & C respectively
A (0,2)
• P=12(0)+14(2)
• P=0+28
• P=28
B (1.3,1.5)
• P=12(1.3)+14(1.5)
• P=15.6+21
• P=36.6
C (2.6,0)
• P=12(2.6)+14(0)
• P=31.2+0
• P=31.2
Hence the point B gives the maximum profit.

12. THANK YOU