Maximizing Investment Returns with Government and Municipal Bonds

How can Robert maximize his investment returns with government and municipal bonds?

Choose the system of inequalities that describes Robert's investment options:

a. x ≥ 2y and y ≤ 5000

b. x ≤ 2y and y ≥ 5000

c. x ≥ 5000 and y ≤ 2x

d. x ≤ 5000 and y ≥ 2x

Answer:

Robert's investment options are described by the inequalities x ≥ 2y (at least twice as much into government bonds as into municipal bonds) and y ≤ 5000 (no more than $5,000 into municipal bonds), which corresponds to option (a). x ≥ 2y and y ≤ 5000.

The system of inequalities that describes Robert's investment options is represented by two conditions based on the information provided:

1. He wants to invest at least twice as much into government bonds than into municipal bonds.

2. He wants to invest no more than $5,000 into municipal bonds.

Letting x be the amount invested into government bonds, and y be the amount invested into municipal bonds, the system of inequalities can be written as:

x ≥ 2y (at least twice as much into government bonds as into municipal bonds)

y ≤ 5000 (no more than $5,000 into municipal bonds)

This corresponds to option (a): x ≥ 2y and y ≤ 5000.