Back to Represent constraints with equations — Problem 2 · Task Set 27

HSA.CED.A.3 Tutor Intake — Constraints, Feasible Regions, and Viable Solutions

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Grade 9·8 problems·~12 min·Common Core Math - HS Algebra·standard·hsa-ced-a-3

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Procedures

A system of constraints for a manufacturing problem is:

$2a + 3b \leq 120$
$a + b \geq 15$
$b \leq 40$
$a \geq 0,\ b \geq 0$

Is the production plan $(a, b) = (50, 20)$ a viable solution?

Yes — $50 + 20 = 70 \geq 15$ , so all constraints are satisfied.

No — $(50, 20)$ violates the time constraint: $2(50) + 3(20) = 160 > 120$ .

Yes — $b = 20 \leq 40$ and both values are non-negative.

No — $(50, 20)$ violates the minimum-total constraint: $50 + 20 < 15$ .