Linear Programming Practice

Identify the slope & equation of the graph

• slope: $2/deposit

  Equation:

  y = 2x+40

• slope: $40/deposit

  Equation:

  y = 40x+40

• slope: $80/deposit

  Equation:

  y = 80x+40

• slope: $80/deposit

  Equation:

  y = 80+40x

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.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 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

Tags

CCSS.HSA.CED.A.3

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

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

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.2

CCSS.HSA.REI.C.6

CCSS.HSA.REI.D.10

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

• 
• 
• 
• 

Tags

CCSS.HSA.REI.D.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

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

CCSS.HSA.REI.D.12

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 . What is the maximum profit that she can earn?

• $15,000
• $21,000
• $18,000
• $25,000

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.2

CCSS.HSA.REI.C.6

CCSS.HSA.SSE.A.1

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 . What combination of soybeans and corn will maximize profit?

• 4 acres of soybeans and 2 acres of corn
• 6 acres of soybeans and 0 acres of corn
• 3 acres of soybeans and 3 acres of corn
• 0 acres of soybeans and 5 acres of corn

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.2

CCSS.HSA.REI.C.6

CCSS.HSA.SSE.A.1

• x = 0, y = 300

• x = 150, y = 150

• x = 100, y 150

• x = 150, y = 100

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.12

CCSS.HSA.REI.C.6