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2 Alg 2 Systems of Inequalities.notebook
1
September 12, 2018
Solving Systems of Linear Inequalities
RECALL:
Steps to Graph a Linear Inequality
Step 1: Graph the boundary (Solid or Dashed)
Step 2: Test a point or y > Shade abovey < Shade below
Step 3: Shade region in which test point is true. Solution to a system is the intersection of the graphs
also referred to as the feasible region.
Learning Target: Solve systems of linear inequalities and apply systems of linear inequalities to real world situations
Example 1)
2 Alg 2 Systems of Inequalities.notebook
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September 12, 2018
Example 2 Find the coordinates of the vertices of the triangle formed by
Example 3 For The Comfort Company, a bed sheet requires 2 pounds of cotton, 9 minutes of dyeing time, and 2 minutes of packaging time. A set of pillowcases requires 1 pound of cotton, 1.5 minutes of dyeing time, and 7.25 minutes of packaging time. Each day, the company has available 110 pounds of cotton, 405 minutes of dyeing time, and 435 minutes of packaging time.
Let: b = the number of bed sheets made per day p = the numbers of sets of pillowcases made per day
Write a system of inequalities that represents the constraints for the situation.
Cotton Packing Time Dying Time
Bed Sheet (b)
Pillowcase (p)
Availability
2 Alg 2 Systems of Inequalities.notebook
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September 12, 2018
Graph the system of inequalities.
Example 3 continued
bed sheets
pillowcases
50
100
150
200
250
0
50 100
150
200
250
300
350
400
Find the vertices of the feasible region.
Example 3 continued
bed sheets
pillowcases
50
100
150
200
250
0
50 100
150
200
250
300
350
400(217.5,0)
(0,60)
(45,0)
(0,270)
(0,110)
(55,0)
23
1
1 & 2
1 & 3
2 Alg 2 Systems of Inequalities.notebook
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September 12, 2018
The Comfort Company's daily revenue will be $12 for each sheet and $8 for each set of pillowcases. Assuming they sell everything the make, how many of each product should the company produce per day to maximize revenue? (plug in all vertices and see which is the greatest)
Example 3 continued Revenue = 12b + 8p
(0, 60): 480
(29, 52): 764 maximum, the company produces 29 bed sheets and 52 pillowcases the company will make $764
(40, 30): 720
(45, 0): 540
(0, 0): 0
Example 4 A farmer has 10 acres to plant in wheat and rye. He has to plant at least 7 acres. However, he only has $1200 to spend and each acre of wheat costs $200 to plant and each acre of rye costs $100 to plant. Moreover, the farmer has to get the planting done in 12 hours and it takes on hour to plant an acre of wheat and 2 hours to plant an acre of rye. If the profit is $500 per acre of wheat and $300 per acre of rye, how many acres of each should be planted to maximize profits?A) Define your variables and translate the constraints into a system of linear inequalities.
(Make a table)
2 Alg 2 Systems of Inequalities.notebook
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September 12, 2018
Example 4
If the profit is $500 per acre of wheat and $300 per acre of rye, how many acres of each should be planted to maximize profits?
Graph the system and find the vertices of the feasible region.
Example 3 continued
Time
Temperature *F
8
16
24
0
Midnight
1 am
2 am
9 am
8 am
7 am
6 am
5 am
4 am
3 am
10 am
11 am
Noon
1 pm
2 pm
9 pm
8 pm
7 pm
6 pm
5 pm
4 pm
3 pm
10 pm
11 pm
Midnight
32
40
48
56
64
72
80
88
96
104