Linear Programming Word Problems- 4th Blue

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

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

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.12

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 ≤ 6
• 2x + 3y ≤ 6
• x + y ≤ 10

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.2

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

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.2

A farmer can plant up to 6 acres of land with soybeans and corn. Her use of a necessary pesticide is limited by federal regulations to 15 gallons for her entire 6 acres. Soybeans require 2 gallons of pesticide for every acre planted and corn requires 3 gallons per acre. The profit the farmer makes by earning $4,000 for every acre of soybeans he plants and $3,000 for every acre he plants with barley can be modeled by P=4000x+3000y .  If x represents acres of soybeans and y represents acres of corns, which inequalities represent the possible solutions to her situation?

• x≥0
  y≥0
  x+y≥6 
  3x+2y≥15
• x≥0 
  y≥0 
  x+y≤6
  2x+3y≤15
• x≥0 
  y≥0 
  4000x+y≤6
  2x+600y≤15
• P=4000x+3000y

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.2

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

Objective quantity:
30x + 50y
Corner that maximizes profit: (0, 6)
What is the profit?

• 300
• 280
• 400
• 240

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.SSE.A.1

Jamie owns a car and a motorcycle. She has at most 12 gallons of gas to be used between the car and the motorcycle. The car's tank holds at most 10 gallons and the motorcyle's tank holds 3 gallons. The mpg (miles per gallon) for the car is 20 mpg and for the motorcycle is 100 mpg. Jamie wants to determine how many gallons of gas should she use which each vehicle to maximize her mileage. What is the objective function?

• M = 3x + 10y

• M = 10x + 3y

• M = 20x + 100y

• M = 100x + 20y