1. Linear Programming
Maximise
P = 3x + 4y

2. Constraints

3. x+5y=20

4. x+y = 8
x+5y = 20

5. x+y = 8
x+5y = 20
x+2y = 16
Remember to also shade the
X<0 and the y<0 areas

6. x+y = 8
x+5y = 20
x+2y = 16
3x + 4y = 20 (Profit line)
3x + 4y = 12
3x + 4y = 6

7. Calculation of P Method 1
Use ‘Profit line’ to determine vertex where P has greatest value. Then calculate co-ordinates of vertex and substitute into profit equation

8. Simultaneous equations
y=8-x
y=4-0.2x
8-x = 4-0.2x
x = 5 and y = 3
You MUST calculate the co-ordinates of the vertex unless your graph is very accurate (BIG graph – at least 2/3 page!)
Simultaneous equations

9. Calculation of P Method 2
Calculate the value of P for every vertex, not just the obvious one
You will still need to calculate the
co-ordinates of the vertex unless your graph is very accurate

10. Your answer… Your answer should clearly state:
Maximum P of ... at (x,y)
where x and y are the co-ordinates you calculated.