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Graph and solve systems of linear inequalitites A-CED 3

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Review graphing linear equations Slope-Intercept form 1. Plot a point on the y-axis (y-intercept) 2.Plot the second point by counting the rise and run (slope) from the y-intercept point.

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Review graphing linear equations Standard Form 1. Put in slope-intercept form (solve for y).

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Review graphing linear equations Vertical Line Horizontal Line

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What does a graph represent? Graphs represent solutions of the equation.

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If I wanted to graph an inequality, how would I represent all possible ordered pairs that are solutions to the problem? SSHADE

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Graphing Inequalities Graph the line using y-intercept and slope Since the problem is an inequality, we need to shade one side of the line to represent all the possible solutions to the inequality.

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If the shaded region represents the solutions to the inequality, how can I check my answer? Pick a point and substitute in the inequality to see if the statement is true.

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Graphing Inequalities I pick the origin (0,0) Therefore the shading is correct.

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Graphing Inequalities I pick the origin (0,0) Shade the side of the line containing the origin.

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Graphing Inequalities NOTE: You can not pick a point that lines on the line. I pick the point (-1,3) Shade the side opposite the point you picked.

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Graphing Inequalities

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Linear Programming Your club plans to raise money by selling two sizes of fruit baskets. The plan is to buy small baskets for $10 and sell them for $15 and buy large baskets for $15 and sell them for $24. The club president estimates that you will not sell more than 100 baskets. Your club can afford to spend up to $1200 to buy baskets. Find the number of small and large baskets you should buy in order to maximize profit.

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0 20 40 60 Objective Function: 5x + 9y (maximum profit) x = # of small baskets y = # of large baskets Total baskets constraint Total spending constraint baskets minimum constraint 80 10 0 20406080 10 0 Feasibility region vertices

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0 20 40 60 Objective Function: 5x + 9y (maximum profit) x = # of small baskets y = # of large baskets 80 10 0 20406080 10 0 Feasibility region (0, 80) (60, 40) (0, 0) (100, 0) vertices

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Objective Function: 5x + 9y (maximum profit) x = # of small baskets y = # of large baskets (0, 80) (60, 40) (0, 0) (100, 0) minimum maximum Check for maximum profit by plugging each vertice of the feasibility region into the objective function.

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