1. October 18 and 19

2. Which car cost under $20,000 with tax?
How can you determine the cost of driving 10,000 miles for a car?
Which cars costs less than $2,000 to drive 10,000 miles?

3. Homework Q and A

4. 3-3 System of Linear Inequalities
Objective:
I can graph two-variable inequalities

5. Steps to graph an inequality
Graph like normal (slope and y-intercept)
Line: Solid (≥, ≤) or Dashed (>, <)?
Test point: Shade the truth
OR When inequality is written in slope-intercept form, < and ≤ shade below line; >, and ≥ shade above the line

6. Steps to graph a system of linear inequalities
Graph each individual inequality with shading
Solution is area shaded twice

7. Steps to graph a system of linear inequalities
Graph each individual inequality with shading
Solution is area shaded twice

8. Solving a System of Inequalities: by graphing
Graph each individual inequality with shading
Solution is area shaded the same # of times as inequalities.
𝒚<−𝟐𝒙+𝟑
𝒚≥ 𝟏 𝟐 𝒙−𝟑
[Y = ]
[◄], [◄], [enter] until inequality is selected
> or ≥
< or ≤
[►], [►], Enter equation
Repeat for all inequalities
𝑥+2𝑦≤4 𝑦≥−𝑥−1

9. A pizza parlor charges $1 for each vegetable topping and $2 for each meat topping. You have $10 to spend on toppings.
You want at least five toppings on your pizza.
How many of each type of topping can you get on your pizza?
𝑣+2𝑚≤10
𝑣+𝑚≥5
p. 153:1-21 odd

10. Day 2…

11. Warm Up Copy and fill in the chart.
Situation
Inequality
Practice more than an hour each day
Write an essay between two and five pages long
Do not spend more than $10 on candy and popcorn
Collect at least 20 snicker bars while trick or treating
P > 1
2 ≤ E ≤ 5
c + p ≤ 10
S ≥ 20
Less than
Less than or equal to
Greater than
Greater than or equal to

12. Homework Q & A

13. Objective: I can solve problems using linear programming.

14. Linear Programming:
Method for finding a minimum or maximum of some quantity given constraints
Constraints: Inequalities
𝒙≥𝟐 𝒚≥𝟑 𝒚≤𝟔 𝒙+𝒚≤𝟏𝟎
Feasible region:
All points that satisfy the constraints
Objective Function:
Quantity you want to maximize or minimize
Vertices of feasible region will be maximum or minimum
2𝑥+𝑦

15. Objective Function:
Find the maximum or minimum points
2𝑥+𝑦
𝒙+𝟐𝒚≤𝟖 𝒙−𝒚≤𝟐 𝒙≥𝟎 𝒚≥𝟎
Vertices:
Test Vertices
Minimum
(0, 0)
2(0) + 0 = 0
(2, 0)
2(2) + 0 = 4
Maximum
(4, 2)
2(4) + 2 = 10
(0, 4)
2(0) + 4 = 4

16. You are printing T-shirts and sweatshirts to sell before homecoming.
You have at most 20 hours to work.
You can spend no more than $600 and you must sell at least 50 items.
T-Shirts
10 minutes to make
Supplies cost $4
Profit $6
Sweatshirts
30 minutes to make
Supplies cost $20
Profit $22
Total
T-Shirts (x)
Sweatshirts (y)
Minutes to work
10x +
30y ≤
20(60) = 1200 4x
20y
Cost + ≤
600 x + y ≥
Number 50
Profit 6x +
22y
Maximize

17. T-Shirts (x)
Sweatshirts (y)
Total
Minutes to work
10x
30y ≤
Cost 4x
20y
≤ 600
Number x y
≥ 50
Profit 6x
22y
maximize + + + +
75 T-shirts, 15 Sweatshirts
Vertices:
Test Vertices
( 50, 0)
6(50)+22(0) =
300
(120, 0)
6(120)+22(0) =
720
(75, 15)
Maximum
6(75)+22(15) =
780
(25, 25)
6(25)+22(25) =
700

18. Paying for College
You have been given $40,000 to invest for a college scholarship. You must invest in both stocks and bonds.
Let x represent the dollars invested in stocks.
Let y represent the dollars invested in bonds.
What inequality can you write to represent the amount of money invested in stocks and bonds?
Bonds
Stocks

19. Paying for College p.160:10-12, 31-37 odd Constraints Pg 339 #1-3, 5
Each investment requires a minimum purchase of $5,000
What are your new inequalities?
Since stocks are more risky you want to at least twice as many bonds as stocks.
What is the inequality?
Constraints
Bonds
Feasible Region
p.160:10-12, odd
Pg 339
#1-3, 5
Stocks