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

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

Profit £P P = 5x + 8y = 2000 P = 5x + 8y = 4000 Maximum Profit at (300, 400) = 1500 + 3200 x (m) y (m) 500 1000 1500 Maximum Profit = £4700 2x + y = 1000 x + 3y=1500 y = 150