Question 1198540: Mutual Funds Suppose that in a certain year, the Phoenix/Zweig Advisors Zweig Total Return fund (ZTR) was expected to yield 3%, and the Madison Asset Management Madison Strategic Sector Premium fund (MSP) was expected to yield 8%. You would like to invest a total of up to $60,000 and earn at least $3500 in interest. Draw the feasible region that shows how much money you can invest in each fund (based on the given yields). (Place ZTR on the x-axis and MSP on the y-axis.)
Find the corner points of the region. (Order your answers from smallest to largest x, then from smallest to largest y. If an answer does not exist, enter DNE.)
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Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! **1. Define Variables**
* Let x be the amount invested in the ZTR fund.
* Let y be the amount invested in the MSP fund.
**2. Formulate Constraints**
* **Investment Budget:** x + y ≤ 60,000 (Total investment cannot exceed $60,000)
* **Interest Earning Constraint:** 0.03x + 0.08y ≥ 3500 (Total interest earned must be at least $3500)
* **Non-negativity Constraints:** x ≥ 0, y ≥ 0 (You cannot invest a negative amount)
**3. Graph the Feasible Region**
1. **Plot the Budget Constraint (x + y ≤ 60,000):**
* Draw a line x + y = 60,000.
* Shade the region below the line (representing investments within the budget).
2. **Plot the Interest Earning Constraint (0.03x + 0.08y ≥ 3500):**
* Draw the line 0.03x + 0.08y = 3500.
* Shade the region above the line (representing investments that meet the interest earning goal).
3. **Plot the Non-negativity Constraints:**
* Shade the region in the first quadrant (x ≥ 0 and y ≥ 0) as we cannot invest negative amounts.
4. **Identify the Feasible Region:**
* The feasible region is the area where all the shaded regions from the above steps overlap.
**4. Find Corner Points**
* **Corner points are the vertices of the feasible region.**
* **Determine the points of intersection of the lines:**
* **Intersection of x + y = 60,000 and 0.03x + 0.08y = 3500:**
* Solve the system of equations.
* One possible solution: (x, y) = (20,000, 40,000)
* **Intersection of x + y = 60,000 and the y-axis (x = 0):**
* (x, y) = (0, 60,000)
* **Intersection of 0.03x + 0.08y = 3500 and the x-axis (y = 0):**
* (x, y) = (116,666.67, 0) - This point is outside the feasible region (x + y > 60,000)
* **Corner Points:**
* (0, 60,000)
* (20,000, 40,000)
**Note:**
* The feasible region is a polygon.
* The exact shape and number of corner points may vary depending on the specific constraints and their intersections.
This analysis provides the framework for finding the feasible region and its corner points. You can further analyze these points to determine the optimal investment strategy based on your risk tolerance and other factors.
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