To solve Sandra's investment problem, we need to maximize her return while satisfying the constraints. This is a linear programming problem. Here's how we can structure and solve it:

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Variables:

• Let $x$ = amount invested in stocks (in dollars).
• Let $y$ = amount invested in bonds (in dollars).
• Let $z$ = amount invested in money market funds (in dollars).

Objective Function:

Maximize $R = 0.15x + 0.10y + 0.08z$, where $R$ is the total return.

Constraints:

1. $x + y + z \leq 50,000$ (Total investment limit).
2. $z \geq 12,500$ (At least $12,500 in money market funds).
3. $y \geq x + z$ (Investment in bonds must be greater than or equal to the sum of stocks and money market funds).
4. $x, y, z \geq 0$ (Non-negativity).

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Let me calculate the optimal investment distribution to maximize Sandra's return..optimize import linprog

Coefficients of the objective function (negative for maximization)

c = [-0.15, -0.10, -0.08] # Maximize return

Coefficients for the inequality constraints

A = [ [1, 1, 1], # Total investment constraint [-1, 0, 0], # Non-negativity constraint for stocks [0, -1, 0], # Non-negativity constraint for bonds [0, 0, -1], # Non-negativity constraint for money market funds [-1, -1, 1], # Bonds >= stocks + money market ] b = [50000, 0, 0, -12500, 0] # Corresponding bounds for inequalities

Bounds for each variable

x_bounds = (0, None) # Stocks must be non-negative y_bounds = (0, None) # Bonds must be non-negative z_bounds = (12500, None) # Money market funds must be >= 12,500

Solve the linear programming problem

result = linprog(c, A_ub=A, b_ub=b, bounds=[x_bounds, y_bounds, z_bounds], method='highs')

Extract results

optimal_investment = result.x max_return = -result.fun # Convert back to positive since we negated c

optimal_investment,The optimal investment strategy for Sandra is as follows:

• Stocks: $37,500
• Bonds: $0
• Money Market Funds: $12,500

Maximum Return:

The maximum return is $6,625.

Would you like a detailed explanation of how this was calculated? Here are 5 related questions to deepen your understanding:

1. What happens if Sandra increases her total investment limit?
2. How do the returns change if the yields on bonds or stocks improve?
3. What are the implications of changing the constraint on bonds being greater than or equal to the sum of other investments?
4. How would adding a new type of investment with a different yield affect the optimization?
5. Can Sandra diversify more effectively if there were a minimum required allocation to bonds?

Tip: Always review investment constraints to see if they align with your financial goals and risk tolerance!