Warm up  Write the equation of a quadratic function with a vertical compression of 0.2 that is shifted left 1 and up 7.  At a clothing store, shirts sell for $10 and sweaters sell for $18. If you bought a total of 20 items and spent $264, how many sweaters did you buy?  If you finish the warm up, study for your quiz!!!

Homework Solutions

Quiz time  Put everything away except for a pencil and a calculator.  You have 15 minutes to complete this quiz. When you are finished, check your work then flip your quiz over on your desk and sit quietly.

THINK/PAIR/SHARE  THINK to yourself: What is a matrix? What do you remember about matrices?  PAIR: Discuss with your partner.  SHARE: With the class.

Solving systems of equations with three variables  Only one way: MATRICES!  Step 1: Standard form  Step 2: Write your coefficient matrix [A] and your solution matrix [B]. Put these in your calculator.  Step 3: Calculate [A] -1 [B].

Example #1 -x + y = 3 5x + y = 9

Example 2: x + y + z = -1 2x – y + 2z = -5 -x + 2y – z = 4

Example #3 5x – 3y – 39 = -2z 4x = -4y + 3z x – 2y + 6z = 14

Example #4:  The first number plus the third number is equal to the second number. The sum of the first number and the second number is six more than the third number. There times the first number minus two times the second number is equal to the third number. What is the sum of the three numbers?

Example #5:  You are training for a triathlon. In your training routine each week, you bike 5 times as far as you run and you run 4 times as far as you swim. One week you trained a total of 200 miles. How many miles did you swim that week?  Write your answer on a sticky note and put it on the wall for a bonus point on your quiz. The point is for effort not accuracy, so show me YOUR OWN answer.

Solving Systems of Inequalities  Only one way!  graphing 1. Put each equation in slope- intercept form and graph 2. Shade to determine the solution region

Example #1 Solve: y ≤ 2x + 3 y ≥ -1/2x + 1

Example #2: Solve: x + 2y ≤ 4 y > -x – 1 x > 2

LINEAR PROGRAMMING  Linear programming is a method for finding a minimum or maximum value of some quantity, given a set of constraints.  It is basically application problems for systems of inequalities.

Linear Programming  Constraints: restrictions on the variables of the objective function in a linear programming problem.  Feasible region: the area bounded by the system of inequalities that contains all the points that satisfy all the constraints.

Linear Programming  Objective function: a model of the quantity you are trying to maximize or minimize.  Vertex (corner) principle of linear programming: If there is a maximum or minimum value of the objective function, it occurs at one or more of the vertices of the feasible region.

Example #1  A city wants to plant maple and spruce trees to absorb carbon dioxide. It has $2100 and 45,000 ft 2 available to plant trees. Using the data from the table, write a system of linear inequalities to model this situation. SpruceMaple Planting Cost $30$40 Area Required 600 ft ft 2 CO 2 absorptio n 650 lb/yr300 lb/yr

Example #1  A city wants to plant maple and spruce trees to absorb carbon dioxide. It has $2100 and 45,000 ft 2 available to plant trees. Graph the feasible region. How many trees of each type should the city plant to maximize absorption?

Example #2 You are screen printing t-shirts and sweatshirts to sell at the Polk County Blues Festival and are working with the following constraints:  You have a most 20 hours to make shirts  You want to spend less than $600 on supplies  You want to have at least 50 items to sell  A 1-color t-shirt takes 10 minutes to make and a 3-color sweatshirt takes 30 minutes to make  Supplies for each t-shirt cost $4 and each sweatshirt $20  You can make a profit of $6 per t-shirt and a profit of $20 per sweatshirt How many t-shirts and sweatshirts should you make to maximize your profit?

Example #2

Journal #1  How are you doing in this class? What are you doing well on? What can you do to improve? What do you like about this class? What would you change? Write a paragraph (at least 5 sentences) and turn it into the box when you are finished. HOMEWORK: WB p. 70 and 74