Problem preview

A-REI.12 Warmup M1-008-A07-V04

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 fiction books and \(y\) be the number of science books. Fiction books cost \(4~\text{dollars}\) each and science books cost \(6~\text{dollars}\) each. You can spend \(\text{at}~\text{most}~48~\text{dollars}\), and you must buy \(\text{at}~\text{least}~3~\text{science}~\text{books}\). Model the feasible region with linear inequalities.

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4x + 6y >= 48, y >= 3, x >= 0, y >= 0

4x + 6y <= 48, y >= 3, x >= 0, y >= 0

4x + 6y <= 48, y <= 3, x >= 0, y >= 0

6x + 4y <= 48, y >= 3, 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