GOZUNTA
Try it now
All courses Math III · A-CED.3 10 of 55
Represent constraints and systems, then interpret viable and non-viable solutions in modeling contexts.

Write a polynomial constraint for a design or revenue context

Problem
Write the polynomial constraint for this design context: area x(20-x) must be at least 75
Your answer
With a free account

Turn browsing into a plan.

Pick an objective, make a session, and give your practice a clear beginning and end.

Create a free account
With paid access

Use the complete visual-support library.

Paid access opens the visual supports attached throughout the full problem bank in your subscribed course or courses.

Compare plans

Hint

Keep the area expression exactly as given, then translate the phrase \(at least 75\) into an inequality.

A design context usually also needs feasible bounds so the factors in the expression stay positive.

Solution walkthrough

01

Use the given area expression

\[A~=~x(20-x)\]

The design context already gives the area as \(x(20-x)\).

02

Translate the wording

\[x(20-x)~\ge~75\]

The phrase \(at least 75\) means the area must be greater than or equal to \(75\).

03

Add the feasibility restriction

\[0<x<20\]

Both side lengths must stay positive, so \(x\) must be between \(0\) and \(20\).

04

State the full constraint

\[x(20-x)~\ge~75~\text{ with }0<x<20\]

The model needs both the inequality and the feasible domain from the geometry.

05

State the final answer

\[A~\text{correct}~\text{polynomial}~\text{constraint}~\text{is}~x(20-x)~\ge~75~\text{with}~0<x<20.\]

A correct polynomial constraint is \(x(20-x)\ge 75\) with \(0<x<20\).

+

Another way

  1. You can first name the two side lengths as \(x\) and \(20-x\), then use area = length times width before applying the inequality.

!

Common mistake

A common mistake is to write only \(x(20-x)\ge 75\) and forget the design restriction that the side lengths must stay positive.