Problem preview

A-REI.12 Warmup M1-008-A07-V02

Graph linear inequalities and systems of linear inequalities as half-plane solution regions.

Model a feasible region from a context

Problem

Let \(x\) be the number of apples and \(y\) be the number of oranges. Apples cost \(1~\text{dollar}\) each and oranges cost \(2~\text{dollars}\) each. You can spend \(\text{at}~\text{most}~20~\text{dollars}\) and buy \(\text{at}~\text{most}~15~\text{fruits}\) total. Model the feasible region with linear inequalities.

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x + 2y <= 20, x + y <= 15, x >= 0, y >= 0

x + 2y >= 20, x + y <= 15, x >= 0, y >= 0

2x + y <= 20, x + y <= 15, x >= 0, y >= 0

x + 2y <= 20, x + y >= 15, x >= 0, y >= 0

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Curriculum context

Course: Math I
Standard: A-REI.12
Category: Algebra
Domain: Reasoning with Equations and Inequalities
Objective: Graph linear inequalities and systems of linear inequalities as half-plane solution regions.
Problem type: Model a feasible region from a context