1. Linear Programming

2. Pens and Pencils
A boy buys x pencils and y pens. Pencils cost 10 pence each and pens cost 20 pence.

3. On your whiteboards
Write an expression for the total cost of x pencils at 10 pence each.
Write an expression for the total cost of y pens at 20 pence each.

4. Pens and Pencils
Pencils cost 10 pence each and pens cost 20 pence. The boy has £1.50 to spend. He must buy at least 4 pencils and at least 1 pen.

5. On your whiteboards… Write an inequality for…
“He must buy at least 4 pencils”
“He must buy at least 1 pen”
“Pencils cost 10 pence each and pens cost 20 pence each. He has £1.50 to spend.”

6. What did you get? “He must buy at least 4 pencils” x ≥ 4
“Pencils cost 10 pence each and pens cost 20 pence each. He has £1.50 to spend.”
10x + 20y ≤ 150

7. Can you write this in a simpler way?
Can you simplify?
10x + 20y ≤ 150
Can you write this in a simpler way?
x + 2y ≤ 15

8. On your grids…
Draw a diagram to show the region defined by these three inequalities:
x ≥ 4
y ≥ 1
x + 2y ≤ 15
REMEMBER TO SHADE THE REGION YOU DON’T WANT!

9. Feasible Region
x = 4
Feasible Region
x + 2y = 15
y = 1

10. Objective Function
Find the maximum number of pens and pencils the boy can buy.
14!

11. 10x + 5y On your whiteboards
If the boy sells pencils for 20 pence and pens for 25 pence write an expression for his profit.
10x + 5y
Use your graph to find the maximum profit the boy can make.

12. How much money?
£1.35
(13 pencils and 1 pen)