Math / Geometry

QuestionMutual Funds Suppose that in a certain year, the Fidelity Nordic Fund (FNORX) was expected to yield 5\%, and the T. Rowe Price Global Technology Fund (PRGTX) was expected to yield $8 \%$ . You would like to invest a total of up to $\$ 80,000$ and earn at least $\$ 5,500$ in interest. Draw the feasible region that shows how much money you can invest in each fund (based on the given yields). (Place FNORX on the $x$ -axis and PRGTX on the $y$ -axis. Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.) \begin{tabular}{|c|c|c|} \hline Inequality & Two Points $(x, y)$ on the Graphed Line & Point ( $x, y$ ) in Shaded Region \\ \hline availabie dollars & $\begin{array}{l} (\square, 0) \\ (0, \square) \end{array}$ & $(\square)$ \\ \hline desired interest & $\begin{array}{l} (\square, 0) \\ (0, \square) \end{array}$ & $(\square)$ \\ \hline $x \geq 0$ & $\begin{array}{l} (\square, 0) \\ (\square, 1) \end{array}$ & $(\square)$ \\ \hline $y \geq 0$ & $\begin{array}{l} (0, \square) \\ (1, \square) \end{array}$ & $(\square)$ \\ \hline \end{tabular}

Studdy Solution

STEP 1

1. The investment in FNORX is represented by $x$ .
2. The investment in PRGTX is represented by $y$ .
3. The total investment should not exceed $80,000.<br />4. The total interest earned should be at least$ 5,500.

STEP 2

1. Formulate the inequalities based on the problem constraints.
2. Identify the intercepts for each inequality.
3. Determine a point in the feasible region.
4. Draw the feasible region on the graph.

STEP 3

Formulate the inequalities based on the problem constraints:
1. Total investment constraint: $x + y \leq 80,000$
2. Interest earned constraint: $0.05x + 0.08y \geq 5,500$
3. Non-negativity constraints: $x \geq 0$ $y \geq 0$

STEP 4

Identify the intercepts for each inequality:
1. For $x + y = 80,000$ : - $x$ -intercept: $(80,000, 0)$ - $y$ -intercept: $(0, 80,000)$
2. For $0.05x + 0.08y = 5,500$ : - $x$ -intercept: Solve $0.05x = 5,500$ to get $x = 110,000$ , so $(110,000, 0)$ - $y$ -intercept: Solve $0.08y = 5,500$ to get $y = 68,750$ , so $(0, 68,750)$

STEP 5

Determine a point in the feasible region:
- Check the point $(0, 0)$ for both inequalities: - $0 + 0 \leq 80,000$ is true. - $0.05 \times 0 + 0.08 \times 0 \geq 5,500$ is false.
- Check the point $(40,000, 40,000)$ : - $40,000 + 40,000 \leq 80,000$ is true. - $0.05 \times 40,000 + 0.08 \times 40,000 = 2,000 + 3,200 = 5,200$ is false.
- Check the point $(60,000, 20,000)$ : - $60,000 + 20,000 \leq 80,000$ is true. - $0.05 \times 60,000 + 0.08 \times 20,000 = 3,000 + 1,600 = 4,600$ is false.
- Check the point $(50,000, 30,000)$ : - $50,000 + 30,000 \leq 80,000$ is true. - $0.05 \times 50,000 + 0.08 \times 30,000 = 2,500 + 2,400 = 4,900$ is false.
- Check the point $(70,000, 10,000)$ : - $70,000 + 10,000 \leq 80,000$ is true. - $0.05 \times 70,000 + 0.08 \times 10,000 = 3,500 + 800 = 4,300$ is false.
- Check the point $(55,000, 25,000)$ : - $55,000 + 25,000 \leq 80,000$ is true. - $0.05 \times 55,000 + 0.08 \times 25,000 = 2,750 + 2,000 = 4,750$ is false.

STEP 6

Draw the feasible region on the graph:
- Plot the lines for the inequalities using the intercepts found in Step 2. - Shade the region that satisfies all inequalities, including $x \geq 0$ and $y \geq 0$ .
The feasible region is determined by the intersection of the constraints, considering the non-negativity of $x$ and $y$ .

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms