Linear Programming and Systems of Inequalities

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

Colin needs to save at least $200 for homecoming. He works 2 jobs earning $9/hour at Wawa and $25/hour mowing lawns. He only has time to work 16 hours before homecoming.

• x + y ≥ 25

  x + y ≤ 9

• 100x + 25 y ≤ 200

  2x + 9y ≤ 16

• x + y ≥ 200

  9x + 25y ≤ 16

• 9x + 25y ≥ 200

  x + y ≤ 16

Which system of linear inequalities is represented by the graph?

• y≤2x-1
  y>-2x+3

• y>2x-1
  y≤-2x+3

• y<2x-1
  y≥-2x+3

• y≤2x-1
  y>2x+3

Which system of inequalities matches the graph?

• y > 2x - 4
  y < 2

• y < 2x - 4
  y < 2

• y > 2x - 4
  y <  2 

• y < 2x - 4
  y <   -2

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); 23

• maximum value at (0, 8); 16

• maximum value at (9, 0); 27

• maximum value at (0, 0); 0

Rachel owns a car and a moped. She has at most 12 gallons of gas to be used between the car and the moped.  The car's tank holds at most 10 gallons and the moped's 3 gallons. The mileage for the car is 20 mpg and for the moped is 100 mpg. 
What are the constraints?

• x≤10, y≤3, x+y≤12

• 0≤x≤10, 0≤y≤3, x+y≤12

• x≥0, y≥0, 10x+3y≤12

• x≤10, y≤3, 10x+3y≤12

Solve the system of inequalities by graphing.

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Solve the system of inequalities by graphing.

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Rewrite this inequality in "y=" form to graph.  3x - 6y > 12

• y > ¹/₂x - 2

• y < -¹/₂x + 2

• y < ¹/₂x - 2

• y > -3x - 2

Which ordered pair(s) is a solution to the given system?

• (5, -5)

• (0,0)

• (-5, -2)

• (3,-3)