An investment broker wants to invest up to $20,000. She can purchase a type A bond yielding a 10% return on the amount invested, and she can purchase a type B bond yielding a 15% return on the amount invested. She wants to invest at least as much in the type A bond as in the type B bond. She will also invest at least $5000 in the type A bond and no more than $8000 in the type B bond. How much should she invest in each type of bond to maximize her return?

I know the equation/function would be R(return) = 0.10x + 0.15y. I also know one of the constraints on this equation is x + y <= 20,000.

What are some other constraints? I don't know how to form them with inequalities.

To determine the additional constraints for the given scenario, we need to consider the investment conditions specified. Let's break down the constraints step by step:

1. The broker wants to invest at least as much in the type A bond as in the type B bond:
This implies that the amount invested in type A bond (x) should be greater than or equal to the amount invested in type B bond (y):
x >= y

2. The broker will invest at least $5000 in the type A bond and no more than $8000 in the type B bond:
This gives us the following constraints:
5000 <= x <= 20000 (lower and upper limit for type A bond)
0 <= y <= 8000 (upper limit for type B bond)

3. The total investment should not exceed $20,000:
This gives us the following constraint:
x + y <= 20000

Now, we have the complete set of constraints for this problem:

x >= y (Investment in type A bond should be at least as much as in type B bond)
5000 <= x <= 20000 (Investment range for type A bond)
0 <= y <= 8000 (Investment range for type B bond)
x + y <= 20000 (Total investment limit)

With these constraints, we can now determine the optimal investment amounts in the type A and type B bonds to maximize the return.