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Accelerated Integrated Geometry 11.1 Inequalities in Two Variables * Graphing Inequalities: 1. Plot reference points. 2. Connect points. a) <,> dashed line b) <,2 solid line 3. Shade solution region: less than - below greater than - above e Examples: Graph each linear inequality. 1 1 y-2 y 2 wes =3 Sx-y>"@ 5x =5x Hy > 54-6 ae ate A BET T ae na Ce | hop ea linear inequality... = 5. x>-2 bi a : ¢ Examples: Graph each absolute value inequality. 7. ys|xj+t 8. y > 3|x| A 10. ys|x+2|-2 i ' o A =< A w al , w “ x “ nN yes 4£2 yor t é id oS z > He ane Cr L LH ‘i _ 2 TI ann 1 6. Write the system of inequalities whose solution is graphed below. [+> V =< _ \ 3 z 7 oe ye at2 a Accelerated Integrated Geometry 11.3 Linear Programming * Linear programming: used to find optimal solutions such as maximum revenue or profit for a real-world situation a) constraints ~ the inequalities contained in the problem b) feasible region - the solution to the set of constraints c) objective function - the function to be maximized or minimized Corner-Point Principle: The maximum and minimum values of the objective function each occur at one of the vertices of the feasible region. * Examples: 1. A farmer wants to plant corn and wheat. He wants to plant no more than 120 acres of both crops. At least 30 acres of corn will be planted. He also wants to plant at least 20 acres of wheat, but no more than 60 acres. The farmer makes a profit of $357.53 for planting corn and $159.31 for planting wheat. a) Write a system of inequalities to represent the constraints. west Xt+y< 120 2 ys-x+120 1 230- 1230 ( 2024 £60 ys20 y2 od b) Graph the feasible region. ¢) Write an objective function for the farmer's total profit and find his : ( overall maximum profit. Ve 357.53 (100) + (54.31 (x) P= 357.53x + 159, Sly Mocinyes > Pz 5 38,939.20 p= 357.53 (30) + 154.31 (6) pe 357.83 ai) rsaai(oq) P= 25753 (30) +59.31(30) P= "20, 284.50 Pz § 21,010.40 Pe 813,912.10 
