any hw questions?

Unit 6 Days 5 and 6 Regular updated Linear Programming.notebook December 01, 2017

Please... Agenda:• have your homework out Warm up• get out your calculator Go over HW• work on warm up Lesson

Work time

Find y when x = 0 and find x when y = 0

4x + 5y = 60 ‐36 = 2x ‐ 3y

Any HW questions?


Write inequalities for the following situations:

Write an essay between two and five pages in length.

Practice more than one hour per day.

The post office is open from nine o'clock until noon.

Do not spend more than $10 on candy and popcorn.

A college fund has $40,000 to invest in stocks and bonds

P > 1

9 < H < 12

C + P < 10

s + b < 40000

2 < E < 5

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I

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LT: I can write and graph inequalities from a real world situation

Words to know: Vertex: Each corner of a regionConstraints: Limitations

The solid boundary line indicates that the region includes the line

The dashed boundary line indicates that the region does not include the line



When you have several inequalities that must be satisfied simultaneously, you have a system. The solution to a system of inequalities is a set of points rather called a feasible region .


Rachel has 3 hours to work on her homework tonight. She wants to spend more time working on mathematics than on chemistry, and she must spend at least a half hour working on chemistry.

a) State the constraints of this system algebraically with x representing mathematics time in hours and y representing chemistry time in hours.

b) Graph your inequalities, shade the feasible region, and label its vertices.



Convert each constraint into an algebraic inequality.

• Rachel has 3 h to work on homework.• She wants to spend more time working on mathematics than on chemistry.• She must spend at least a half hour working on chemistry.

x = # hours Mathy = # hours Chem


How to graph systems of inequalities on your calculator...

• Put the equation into y = as if there were no inequality.

• SHADE the opposite region (it is more difficult to see the vertices of a feasible region if everything is dark.) For ≥, on calc shade below; for ≤ on calc shade above.

• To shade, go to the left of the = and hit enter until you get to the opposite shading.

LT: I can write and graph inequalities from a real world situation Teachersnot sure if we want this or not...I think it's ok to skip on calc.


The solution to this system is all points in the interior of a triangle with vertices(1.5, 1.5), (2.5, 0.5), and (0.5, 0.5), and the points on the lower and right edges of thetriangle.

Any point within this region represents a way that Rachel could divide hertime. For example, (1.5, 1) means she could spend 1.5 h on mathematics and 1 h onchemistry and still meet all her constraints.

Notice, however, that (0.5, 0.5) is not asolution to the system, even though it is a vertex of the feasible region. The point(0.5, 0.5) does not meet the constraint x > y.


There are two constraints that we don't typically write. We call these the common

sense constraints: x ≥ 0 and y ≥ 0



Situation #1. PARTY NUTS.Zark is buying peanuts and cashews for a party. He can spend no more than $24. Peanuts cost $2 per pound and cashews cost $3 per pound. Let x = number of pounds of peanuts Let y = number of pounds of cashews

Inequality:____________________

1. Which of the following is a solution of the inequality? a. (2,8) b. (4,6) c. (8.2)2. What is the greatest number of pounds of peanuts that Zark can buy?3. If x = 6 lb, what are all the possible amounts of Cashews he can buy?


Situation #2. DO YOU WANNA DANCE? Student Council is selling tickets to the Valentine Dance. Tickets cost $5 per person or $8 per couple. To cover expenses, at least $1200 worth of tickets must be sold.Let x = number of $5 tickets soldLet y = number of $8 tickets sold

Inequality:____________________

7. Which of the following is a solution of the inequality? a. (160,40) b. (40,160) c. (80,80)8. How many $8 tickets must be sold if no $5 tickets are sold?9. If x = 80 tickets, what are all possible values of y?



Situation1. SOMETHING FISHY.The owner of Fred’s Fish Market orders Cod and Salmon. He wants to buy at least 50 pounds of fish but cannot spend more than $300. Cod is $4 per pound and salmon is $7 per pound.

Let x = number of pounds of codLet y = number of pounds of salmon

Inequality #1:____________________

Inequality #2:____________________

Which of the following are solutions?a. (40,15) b. (50,18) c. (30,20) d. (55,8) e. (20,35)

Situation #3. RUB-A-DUB-DUBKara is filling her bathtub. The cold water flows in at a rate of 4 gal/min. The hot water flows in at a rate of 3 gal/min. Kara wants no more than 60 gal of water in the tub.Let x = amount of time the cold water is onLet y = amount of time the hot water is on

Inequality:____________________

4. Which of the following is a solution of the inequality? a. (5,16) b. (10.4) c. (12,5)5. How many minutes will it take to get 60 gal of water if only cold water is turned on?6. If x = 3 min, what are all possible of values of y?

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