What we do is use test points to determine which side of the line we are concerned about. Select a point on one side of the line and sub it into the inequality if the inequality is solved that is the side of the line we shade
The area we shade is called the Solution Region When we graph a line the Cartesian plane is cut into tow halves called Half Planes A Continuous line is a line that contains real numbers. All numbers are included so the line is solid (continuous).
3. Using the Graphs to Solve Problems FM20.8 Demonstrate understanding of systems of linear inequalities in two variables.
3. Using the Graphs to Solve Problems What combinations of boats should the company make each day?
Is every point in the region a possible solution to the problem? How would the graph change if fewer than 25 boats were made each day? All whole points with whole number coordinates in the solution region are valid, but are they all reasonable?
Practice Ex. 6.3 (p.317) #1-4 odds in each, 5-10 #4-12
4. Creating Optimization Problems FM20.8 Demonstrate understanding of systems of linear inequalities in two variables.
4. Creating Optimization Problems Optimization Problem – A problem where a quantity must be maximized or minimized following a set of guidelines or conditions. Constraint – A limiting condition of the optimization problem being modeled, represented by a linear inequality. Objective Function – In an optimization problem, the equation that represents the relationship between the two variables in the system of linear inequalities and the quantity to be optimized. Feasible Region – The solution region for a system of linear inequalities that is modeling an optimization problem.
6. Determine the Max and Min FM20.8 Demonstrate understanding of systems of linear inequalities in two variables.
6. Determine the Max and Min The process that we have been developing and will finish today is called linear programming Linear Programming is used to find the solution in the feasible region result in the optimal solutions of the objective functions
What happens if the optimal points (intersection points of constraints) do not land on a whole number coordinate? We solve the two inequalities like they where linear equations using the substitution or elimination strategies. This gives us the point where the two lines intersect.