Linear Programming

Sarah makes small purses (x) and big purses (y). She can make no more than 8 purses a week.

Which inequality represents the situation?

• x + y ≤ 8

• x + y > 8

• 2x + 3y ≤ 6

• x + y ≤ 10

It takes Sarah 2 hours to make small purses and 3 hours to make big purses. She has a maximum of 18 hours a week. Which inequality represents this situation?

• 2x + 3y ≤ 18
• x + y ≤ 6
• x + y ≤ 9
• 3x + 2y ≤ 18

Write the system of inequalities
Carlos works at a movie theater selling tickets. The theater has 300 seats and charges $7.50 for adults and $5.50 for children. The theater expects to make at least $2000 for each showing.  

• x+y≤300
  7.5x+5.5y≥2000
• x+y<300
  7.5x+5.5y≥2000
• x+y≤300
  7.5x+5.5y≤2000
• x+y>2000
  7.5x+5.5y≤300

Which of the following is not a solution to this system of inequalities?

• (0,-1)
• (0,3)
• (4,0)
• (6,-2)

Tags

CCSS.HSA.REI.D.12

Solve the system of inequalities. The feasible region is shown by the darkest blue shading.

• 
• 
• 
• 

Tags

CCSS.HSA.REI.D.12

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 variables you need to define?

• x is gas, y is mileage
• x is car, y is moped
• x is gas, y is moped
• x is car, y is mileage

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

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

• P = 30x + 50y
• P = 50x + 30y

Which of the following inequalities matches the given graph?

• x ≥ -1
• x ≤ -1
• x > -1
• x < -1

Tags

CCSS.HSA.REI.D.12

Which of the following inequalities matches the given graph?

• y ≤ -3/4 x + 3
• y ≥ -3/4 x + 3
• y < -3/4 x + 3
• y > -3/4 x + 3

Tags

CCSS.HSA.REI.D.12