To find out how much Jamaal should invest in each bank to earn the most interest, we can solve this problem using linear programming.
Let's represent the amount Jamaal invests in City Bank as "x" and the amount he invests in State Bank as "y."
We are given the following information:
- Jamaal wants to invest at least $4000 in City Bank but no more than $16000. So we have the constraint: 4000 ≤ x ≤ 16000.
- State Bank does not insure more than $8000. Therefore, we have the constraint: y ≤ 8000.
- Jamaal plans to invest up to $23000 in total. So we have the constraint: x + y ≤ 23000.
Now let's determine the objective function to maximize the interest earned:
- The interest earned at City Bank is 5% of the invested amount, so the interest earned at City Bank is 0.05x.
- The interest earned at State Bank is 7% of the invested amount, so the interest earned at State Bank is 0.07y.
- Therefore, the total interest earned is 0.05x + 0.07y.
To find the maximum amount of interest, we need to solve this linear programming problem.
Once we solve, we can determine the respective values of x and y, which will tell us how much Jamaal should invest in each bank, and the resulting maximum interest earned.
I'll now solve the linear programming problem using an optimization tool.