LP GRAPHICAL METHOD

Solve the following LPP. 1. Minimize: C = 2x + 3y Subject to: 5x + 2y 2 20 x + 4y s 22 x + 2y 28 x 20, y 20 2. Maximize: P = 5x + 2y Subject to: 4x + y s 40 x + 3y 2 30 2x + y s 30 x20, y 20 3. A steel producer makes two types of steel: regular and special steel. A ton of regular steel requires 2 hours in the open-hearth furnace and 3 hours in the soaking pit; a ton of special steel requires 2 hours in the open-hearth furnace and 5 hours in the soaking pit. The open-hearth furnace is available 8 hours per day and the soaking pit is available for 15 hours per day. The profit on a ton of regular steel is Php4,000 and it is Php6,000 on a ton of special steel. Determine how many tons of each type of steel should be made to maximize the profit, considering that demand on regular steel is at least 1 ton. 4. Determine if the given LPP is unbounded, infeasible, or has multiple solutions: Maximize: 3x + 5y Subject to: 2x + y 2 7 x+y26 x + 3y 29 x20, y20