Feasible Regions

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

• (0, 0), (0, 6), (6, 2), (8, 0)
• (0, 0), (6, 0), (2, 6), (0, 8)

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

The corners of a feasible region are (-3,3), (-2,6), (0,6), and (1.5,3). The objective function is: P = 4x - 2y. Find the maximum and minimum values of the function for this region.

• The maximum value is 0 at (0, 6). The minimum value is - 20 at (-3, 3).

• The maximum value is 0 at (-3, 3). The minimum value is - 20 at (0, 6).

• The maximum value is 0 at (-2, 6). The minimum value is - 20 at (1.5, 3).

• The maximum value is 0 at (1.5, 3). The minimum value is - 20 at (-2, 6).

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.2

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.1

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

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.SSE.A.1

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.2

Objective quantity:
P = 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

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.2

CCSS.HSA.CED.A.3

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 . After graphing the inequalities in #8, the corner points are found to be: (0. 0), (6. 0), (0, 5), (3,3). What is the maximum profit that can be earned?

• $15,000

• $24,000

• $18,000

• $25,000

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 . After graphing the inequalities in #8, the corner points are found to be: (0. 0), (6. 0), (0, 5), (3,3). What combination of soybeans and corn from the previous problem did you discover 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