INTEGRATED MATH 2 INEQUALITIES IN TWO VARIABLES LESSON OBJECTIVES: 1)Graph the solution set of a linear inequality in two variables. 2)Graph the solution.

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Presentation transcript:

INTEGRATED MATH 2 INEQUALITIES IN TWO VARIABLES LESSON OBJECTIVES: 1)Graph the solution set of a linear inequality in two variables. 2)Graph the solution set of a system of inequalities in two variables.

3)Solve linear programming problems involving two independent variables.

Many problems that arise in making plans for a business involve functions with two or more variables. For example, income for the Old Dominion Music Festival is given by the function I = 8a + 12 g, where a is the number of admission tickets sold in advance and g is the number of tickets sold at the game.

If expenses for operating the two-day festival total $2,400, then solutions of 8a + 12g = 2,400 give (a, g) combinations for which festival income will equal operating expenses. But festival organizers are probably interested in earning more than $2,400 from ticket sales.

They want solutions to the inequality 8a + 12g > 2,400. a.For each point on the diagram, give the (a, g) coordinates and the festival income from that combination of tickets sold in advance and tickets sold at the gate.

A.I = 8(100) + 12(200) = 3,200 B.I = 4,600 AT (200, 250) C.I = 5,400 AT (300, 250) D.I = 3,800 AT (250, 150) E.I = 3,000 AT (300, 50) F.I = 2,000 AT (250, 0) G.I = 2,200 AT (200, 50) H.I = 1,400 AT (100, 50) I.I = 2,200 AT ( 50, 150)

Internet Calculator Online Use this website to graph your inequalities!! It is a free website and is very useful if you do not have a graphing calculator.

HOMEWORK!! Complete the two homework pages. You are allowed to work in groups for the homework. Have a great day!!