1. Linear Programming Constraints: Wants maximum profit £P P = 5x + 8y
Carpet firm makes 2 types of stair carpet: Standard & Heavy Duty.
Has monthly order for 150m of Heavy Duty.
Can sell all it makes.
Heavy Duty
Standard
Carpet Types
0.3 h/m
0.2 h/m
0.1 h/m
Process A
0.4 h/m
Process B
Profit
£8 per metre
£5 per metre
(x m)
(y m)
Maximum/Month
150 hours
200 hours
Constraints:
y ³ 150
0.1x + 0.3y £ 150
0.4x + 0.2y £ 200
x + 3y £ 1500
4x + 2y £ 2000
2x + y £ 1000
Wants maximum profit £P
P = 5x + 8y

2. y ³ 150
x + 3y £ 1500
2x + y £ 1000 x y
1500
900 x y
500
200
500
200
1000
600
x (m)
y (m)
500
1000
1500
2x + y = 1000
x + 3y=1500
Possibilities
y = 150

3. Profit £P P = 5x + 8y = 2000 P = 5x + 8y = 4000
Maximum Profit at (300, 400) =
x (m)
y (m)
500
1000
1500
Maximum Profit = £4700
2x + y = 1000
x + 3y=1500
y = 150