Algebra 2 Systems of Equations

Solve the system of inequalities by graphing.

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Cullin needs to save at least $100 for homecoming.  He works 2 jobs earning $8/hour at Culvers and $25/hour mowing lawns.  He only has time to work 14 hours before homecoming. 

• x + y  ≥ 25
  x + y ≤ 8

• 100x + 25 y ≤ 100
  2x + 8y ≤ 14

• x + y ≥ 100
  8x + 25y ≤ 14

• 8x + 25y ≥ 100
  x + y ≤ 14

Write the system of inequalities
Eiko is drawing caricatures at a fair for 8 hours (480 minutes). She can complete a small drawing in 15 minutes and charges $10 for the drawing. She can complete a larger drawing in 45 minutes and charges $25 for the drawing. Eiko hopes to make at least $200 at the fair. 

• 10x+15y≤480
  45x+25y≥250

• 10x+25y≤200
  15x+45y≤480

• 10x+25y>200
  15x+45y<480

• 10x+25y≥200
  15x+45y≤480

Find the values of x and y that maximize the objective function P = 3x + 2y for the graph. What is the maximum value?
   

• maximum value at (5, 4); 32

• maximum value at (0, 8); 16

• maximum value at (9, 0); 27

• maximum value at (0, 0); 0

• x = 0, y = 300

• x = 150, y = 150

• x = 100, y 150

• x = 150, y = 100

Sarah makes $30 for each small purse (x) and $50 for each big purse (y). What is the objective function?

• P = 30x + 50y

• P = 50x + 30y

In other words...what are the vertices of the feasible region?

• (0, 0), (0, 6), (6, 2), (8, 0)

• (0, 0), (6, 0), (2, 6), (0, 8)

Which are vertices of the feasible region?

• (0, 3) (3, 0) (5, 8)

• (0, 6) (3, 5) (6, 5)

• (3, 3) (8, 5) (5, 8)

• (0, 5) (6, 0) (3, 3)

Solve!

• (2,7,5)

• (-8,7,5)

• (-8,2,5)

• (-3,2,5)

Solve!

• (1,1,1)

• (6, -8, 36)

• (6,-8, 20)

• (6,-8,-20)