AFDA.AF.3.a
Represent and interpret contextual problems requiring optimization with systems of linear equations or inequalities.
Example Problems
It takes 12 hours and $250 to paint a single-family home, and it takes 80 hours and $600 to paint a commercial building.
A painting company has less than $70000 to paint these properties, and it wants to spend at most 900 hours to do so.
Let denote the number of single-family homes they paint and the number of commercial buildings they paint.
Write a system of inequalities that represents the following conditions:
1. An inequality that represents the condition based on the number of dollars the company can spend.
2. An inequality that represents the condition based on the number of hours the company wants to spend.
A painting company has less than $70000 to paint these properties, and it wants to spend at most 900 hours to do so.
Let denote the number of single-family homes they paint and the number of commercial buildings they paint.
Write a system of inequalities that represents the following conditions:
1. An inequality that represents the condition based on the number of dollars the company can spend.
2. An inequality that represents the condition based on the number of hours the company wants to spend.
It takes 15 hours and $250 to build a bicycle, and it takes 100 hours and $300 to build a scooter.
A company has less than $80000 to build these products, and it wants to spend at most 500 hours to do so.
Let denote the number of bicycles they build and the number of scooters they build.
Write a system of inequalities that represents the following conditions:
1. An inequality that represents the condition based on the number of dollars the company can spend.
2. An inequality that represents the condition based on the number of hours the company wants to spend.
A company has less than $80000 to build these products, and it wants to spend at most 500 hours to do so.
Let denote the number of bicycles they build and the number of scooters they build.
Write a system of inequalities that represents the following conditions:
1. An inequality that represents the condition based on the number of dollars the company can spend.
2. An inequality that represents the condition based on the number of hours the company wants to spend.
It takes and to assemble a smartphone, and it takes and to assemble a tablet.
An electronics company has less than to assemble these devices, and it wants to spend at most to do so.
Let denote the number of smartphones they assemble and the number of tablets they assemble.
Write a system of inequalities that represents the following conditions:
1. An inequality that represents the condition based on the number of dollars the company can spend.
2. An inequality that represents the condition based on the number of hours the company wants to spend.
An electronics company has less than to assemble these devices, and it wants to spend at most to do so.
Let denote the number of smartphones they assemble and the number of tablets they assemble.
Write a system of inequalities that represents the following conditions:
1. An inequality that represents the condition based on the number of dollars the company can spend.
2. An inequality that represents the condition based on the number of hours the company wants to spend.
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