Linear Inequalities in Two Variables and Linear Programming

Jina is raising money for a charity. She makes either 18 telephone calls per day or 10 homes visits per day. Jina wants to contact at least 100 people next week. This situation can be represented by the following system. x = number of days making telephone calls and y = number of days making home visits. Which is true?  x+y≤7    18x+10y≥100

• Jina can reach her goal by making only home visits.

• Jina can reach her goal with only 2 days of telephone calls

• If Jina does home visits for 4 days, she only needs 2 days of telephone calls. 

• If Jina makes telephone calls for 5 days, she only needs 1 day of home visits. 

Luka and Dana are making cookies for the Westland Pantry. They only have up to 6 hours to bake! They can bake 32 chocolate chip cookies in an hour (x), and 20 snickerdoodle cookies in an hour (y). They need to make at least 150 cookies. Which one of these is a valid solution?

• (3, 2)

• (1, 4)

• (2, 8)

• (5, 1)

You can work no more than 10 hours each week at your two jobs. Housecleaning pays $5 per hour and your sales job pays $8 per hour. You need to earn at least $56 each week to pay your bills. Write a system of inequalities to represent this scenario.

• (7,4)

• (3,10)

• (10,1)

• (8,5)

Garima likes her job as a baby-sitter (b), but it pays only Rs300 per hour. She has been offered a job as a tutor (t) that pays Rs600 per hour. Because of school, her parents only allow her to work a maximum of 15 hours per week, but she needs to make at least Rs6600 per week. Which system of inequalities below correctly models Joann's situation?

• b + t < 15

  3b + 6t > 66

• b + t > 15

  3b + 6t < 66

• 3b + 6t > 15

  b + t < 66

• 300b + 600t < 15

  b + t < 66

______ ___________ is a method for finding maximum or minimum values of a function for a region defined by a system of linear inequalities.

In linear programming, the _____ _____ is the intersection of the graphs in a system of constraints.

A(n) ________ is a mathematical sentence that contains the symbols <, ≤, >, ≥, or ≠.

the shaded area is the ...

• maximize

• solution region

• intersection

• boundary line

A method for solving a problem with several conditions or constraints that can be represented as linear equations or inequalities.  

• linear programming

• looking inside

• maximize

• one-variable equation