Interpreting Linear Inequality Systems

A farmer has asked you for advice on the best strategy for planting wheat and corn on her 500-acre farm. To make it through harvest time, each acre of wheat she plants will require 1 person-day of labor and other expenses of $20. Each acre of corn she plants will require 5 person-days of labor and expenses of $30. The farmer has $11,400 and 1480 person-days of labor available, and she expects to make a profit of $90 per acre of wheat and $120 per acre of corn. If x = acres of wheat and y = acres of corn, which of the following is NOT a constraint?

• x + y ≤ 500

• 20x + 30y ≤ 11,400

• y ≥ 5x + 30

• x + 5y ≤ 1480

Ms. Savva is ordering pizzas and breadsticks for a school party and has a budget of no more than $81. An order of breadsticks costs (x) $7 and a pizza costs (y) $13. 7x + 13y ≤ 81 Given Ms. Savva's budget, which of the following give a viable option she can purchase for the school party?

• 7 breadstick and 3 pizzas

• 3 breadstick and 4 pizzas

Fatima likes her job as a baby-sitter, but it pays only $5 per hour. She has been offered a job as a tutor that pays $8 per hour. Her parents will allow her to work a maximum of 15 hours per week. Write a system of linear inequalities to determine many hours Fatima can baby-sit and tutor and make at least $100 per week.

• b + t < 15

  5b + 8t > 100

• b + t > 15

  5b + 8t < 100

• 5b + 8t > 15 b + t < 100

• 5b + 8t < 15 b + t < 100

Solve each of the following systems of linear inequalities a graphing approach. Verify using a graphing calculator. Which of following are the vertices?

• (2, 0), (4, 5), (6, 0)

• (2, 0), (3, 5), (0, 6)

• (0, 2), (3.5, 4.5), (6, 2)

• (0, 0), (3, 5), (6, 0)

The girls’ swim team is hosting a fund raiser. They would like to raise at least $500. They are selling candles for $5 and flower arrangements for $6. The girls estimate that at most they will sell 200 items.

Which answer represents the system?

Select the correct graph for each inequality.

• A

• B

• C

• _D

• x > -2 , y ≤ -x + 2 , y ≤ 1/2 x + 1

• x > -2 , y ≥ -x + 2 , y ≥ 1/2 x + 1

• x > -2 , y ≥ -x + 2 , y ≤ 1/2 x + 1

• x > -2 , y ≤ -x + 2 , y ≥ 1/2 x + 1

• A

• B

• C

• D

Which point below is NOT part of the solution set?

• (0, 0)

• (-10, 20)

• (3, 5)

• (0, -2)