Solving/interpreting linear inequalities in two variables

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

The North Decatur Band is doing a fundraiser selling butter braids attempting to earn $1,000. They are selling regular butter braids and a giant cinnamon roll braid. The regular butter braids are represented by x and cost $17 each and the giant cinnamon roll costs $30 each and is represented by y.

17x + 30y = 1000

What is the domain?

• [33.33, 0]

• [58.82, 0]

• [0, 58.82]

• [0, 33.33]

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

• $x+y\le300$
  $7.5x+5.5y\ge2000$
  

  $y\ge0$
  $x\ge0$
  

• $x+y<300$
  $7.5x+5.5y\le2000$
  $x\ge0\ \ \ \ \ \&\ y\ \ge0$
  

• $x\ge0$
  $x+y\ \ge2000$

  $y\ge0$
  $7.5x+5.5y\le\ 300$
  

Write a system of inequalities to model the following situation:
"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

Marsha is buying plants and soil for her garden. The soil cost $4 per bag, and the plants cost $10 each. She wants to buy at least 5 plants and can spend no more than $100. Write a system of inequalities to model the situation.

• 4s+10p≤100
  s+p≥5
• 4s+10p≤100
  p≥5
• s+p≤100
  4s+10p≥5
• 4+p≤10
  5+s≤100

If the vertices of the feasible region are (0,0); (2,5); (6,2); and (4,4), which coordinate maximizes the objective function:

P = 2x+3y

• (0,0)

• (2,5)

• (6,2)

• (4,4)

Objective function:

P = 30x + 50y

Corner Points: (0, 0) (8, 0) (6, 2) (0, 6)

What is the maximum profit?

• 300

• 280

• 400

• 240

Alexa is printing brochures for his new business and needs printer cartridges. Christian needs at least 50 cartridges. Black and white cartridges are $10 and color cartridges are $15. Alexa only budgeted $500 for the project. Which system represents this situation?

• x+y≥50

  10x+15y≤500

• x+y≤50

  10x+15y≥500

• 10x+15y≥50

  x+y≤500

• 10x+15y≤50

  x+1y≥500

• Lorenzo can use four 46 cent stamps and six 20 cent stamps

• Lorenzo can use five 46 cent stamps and four 20 cent stamps.

• If Lorenzo uses six 46 cent stamps, he only needs to use one 20 cent stamp

• If Lorenzo uses twelve 20-cent stamps, he only needs to use one 46-cent stamp.

Monu and Bala want to improve their yards by planting hostas and ivy. The cost of one hosta is Rs80 and the cost of one pot of ivy is Rs120. They do not want to spend more than Rs600 and they want to buy at least 6 plants. Write a system that represents the possible number of hosta x, and ivy plants y, that could be sold to meet these conditions.

• 8x + 12y ≥ 60

  x + y ≥ 6

• 8x + 12y ≤ 60

  x + y ≥ 6

• 8x + 12y ≤60

  x + y ≤ 6

• 8x + 12y ≥ 60

  x + y ≤6