Problem preview

A-CED.3 Warmup M1-003-A03-V02

Represent constraints with equations, inequalities, and systems; interpret viable and non-viable solutions in context.

Test whether a point is viable for a system of constraints

Problem

At a garden, \(x\) large seed bundles and \(y\) small seed bundles are nonnegative whole-number counts. Test \((6,~4)\) against \(C_{1}\): \(5x~+~3y~\le~35\); \(C_{2}\): \(x~+~y~\le~12\); \(C_{3}\): \(x~\ge~0\); and \(C_{4}\): \(y~\ge~0\). State the constraints it satisfies and violates, then determine whether the proposal is viable.

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C1, C2, C3, and C4 are satisfied; none is violated; the proposal is viable

C1, C3, and C4 are satisfied; C2 is violated; the proposal is not viable

C2, C3, and C4 are satisfied; C1 is violated; the proposal is not viable

C3 and C4 are satisfied; C1 and C2 are violated; the proposal is not viable

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Curriculum context

Course: Math I
Standard: A-CED.3
Category: Algebra
Domain: Creating Equations
Objective: Represent constraints with equations, inequalities, and systems; interpret viable and non-viable solutions in context.
Problem type: Test whether a point is viable for a system of constraints