October 18 and 19

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?

Homework Q and A

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

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

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

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

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

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

Day 2…

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

Homework Q & A

Objective: I can solve problems using linear programming.

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

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

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

T-Shirts (x) Sweatshirts (y) Total Minutes to work 10x 30y ≤ 1200 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

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

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, 31-37 odd Pg 339 #1-3, 5 Stocks