Download presentation

Published byLinda Washington Modified over 6 years ago

1
**3.3 Systems of Linear Inequalities -graphing -linear programming**

2
Solution The solution to a system of inequalities is the area where the shaded regions overlap. Any point in this area will work for BOTH of the inequalities.

3
**To Graph a Linear Inequality:**

ToTo Graph a Linear Inequality: Solve the inequality for y *Remember: if dividing or multiplying by a negative to switch the sign Graph the line * Plot the y-intercept then use the slope to find the next point * Dotted line for < and > * Solid line for < and > 3) Pick a point not on the line 4) Plug the point into the inequality *True = shade the side with the point *False = shade the other side of the line Graph a Linear Inequality:

4
Graph the system y < -2x + 4 x > -3

5
Graph the system y < 3x – 6 y > -4x + 2

6
Graph the system -2y < 4x + 2 y > x + 2 y < 4

7
Linear Programming -Used to find the maximum or minimum value of an objective function. -The maximum or minimum must occur at a vertex of the feasible region. -Find the feasible region by graphing all constraints. The feasible region is found where all of the shading overlaps. -Determine the coordinates of the vertices of the feasible region and plug these into the objective function to find the minimum or maximum value. -Unbounded regions may have no maximum or minimum.

8
**Find the maximum and minimum value of z = 3x + 4y subject to the following constraints:**

9
**So the corner points are (2, 6), (6, 4), and (–1, –3).**

10
**Linear Programming Problem**

The available parking area of a parking lot is 600 square meters. A car requires 6 sq. meters of space and a bus requires 30 sq. meters of space. The attendant can handle no more that 60 vehicles. If a car is charged $2.50 to park and a bus is charged $7.50, how many of each should the attendant accept to maximize profit?

11
Linear Programming Jeff makes 2 types of wood clocks to sell at local stores. It takes him 2 hours to assemble a pine clock, which requires 1 oz. of varnish. It takes 2 hours to assemble an oak clock which takes 4 oz. of varnish. Jeff has 16 oz. of varnish and he can work 20 hours. He makes a $3 profit on pine clocks and a $4 profit on oak clocks. How many of each type should he make to maximize profit?

12
**Linda makes pumpkin bread and banana bread to sell at a bazaar**

Linda makes pumpkin bread and banana bread to sell at a bazaar. A loaf of pumpkin bread requires 2 cups of flour and 2 eggs. A loaf of banana bread takes 3 cups of flour and 1 egg. Linda has 12 cups of flour and 8 eggs. She makes a $2 profit per loaf of pumpkin bread and $2 profit per loaf of banana bread. How many loaves of each should she make to maximize profit?

13
**A biologist needs at least 40 fish for her experiment**

A biologist needs at least 40 fish for her experiment. She cannot use more than 25 perch or more than 30 bass. Each perch costs $5 and each bass costs $3. How many of each type of fish should she use in order to minimize her cost?

14
**-organize your information (charts help!) **

Step by step! -Identify your variables -organize your information (charts help!) -write your objective function -write all constraints -graph all constraints -determine the vertices of the feasible region -plug the coordinates of the feasible region into the objective function -determine the maximum or minimum value -state your answer

15
Linear programming! Your factory makes fruit filled breakfast bars and granola bars. For each case of breakfast bars you make $40 profit. For each case of granola bars you make $55 profit. You have a maximum of 150 machine hours and it takes 6 machine hours for each case of granola bars and 2 machine hours for each case of breakfast bars. You have only 155 hours of labor available and it takes 5 hours to make one case of breakfast bars and 4 hours for a case of granola bars. How many cases of each should you produce to maximize profit?

Similar presentations

© 2021 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google