A couple has 20,000 dollar to invest for their child's...

A couple has 20,000 dollar to invest for their child's future college expenses. Their accountant recommends placing at least 12,000 dollar in a high-yield mutual fund and at most 6000 dollar in a low-yield mutual fund. (a) Use $x$ to denote the amount of money placed into the high-yield fund. Use $y$ to denote the amount of money placed into the low-yield fund. Write a system of linear inequalities that describes the possible amounts in each type of account. (b) Graph the region that represents all possible amounts the couple could place into each account if they wish to follow the accountant's advice.

A couple has 20,000 dollar to invest for their child's future college expenses. Their accountant recommends placing at least 12,000 dollar in a high-yield mutual fund and at most 6000 dollar in a low-yield mutual fund.
(a) Use $x$ to denote the amount of money placed into the high-yield fund. Use $y$ to denote the amount of money placed into the low-yield fund. Write a system of linear inequalities that describes the possible amounts in each type of account.
(b) Graph the region that represents all possible amounts the couple could place into each account if they wish to follow the accountant's advice.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Feasible Region

The feasible region is the collection of all points in the coordinate plane that satisfy all the constraints defined by a system of inequalities. This region represents all possible solutions to the modeled problem and is often used in optimization to identify the best choices under given restrictions.

Linear Inequalities

Linear inequalities are mathematical expressions that involve a linear function and inequality signs (such as ?, ?, <, >). They are used to represent constraints or conditions where a variable must fall within a certain range, making them essential for modeling scenarios with limits or bounds.

System of Linear Inequalities

A system of linear inequalities consists of multiple inequalities that must be satisfied simultaneously. The set of solutions is the common intersection of the solution sets of each individual inequality, which is crucial in problems where several conditions need to be met at the same time.

Graphing Constraints

Graphing constraints involves plotting each inequality on a coordinate plane, using boundary lines (where the inequality holds as an equality) and shading the region that meets the inequality condition. This visual representation helps identify the feasible region where all constraints overlap.

Transcript

Please give Ace some feedback