Answered

At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Get quick and reliable solutions to your questions from a community of experienced professionals on our platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

An investor has up to $250,000 to invest in three types of in-vestments. Type A pays 8% annually and has a risk factor of0. Type B pays 10% annually and has a risk factor of 0.06.Type C pays 14% annually and has a risk factor of 0.10. Tohave a well-balanced portfolio, the investor imposes the fol-lowing conditions. The average risk factor should be nogreater than 0.05. Moreover, at least one-fourth of the totalportfolio is to be allocated to Type A investments and at leastone-fourth of the portfolio is to be allocated to Type B invest-ments. How much should be allocated to each type of invest-ment to obtain a maximum return?

Sagot :

Answer:

Answer is explained below in the explanation section.

Explanation:

Solution:

An investor has up to $250,000 to invest in three types of investment.

Type A pays 8% annually and has risk factor of 0.

Type B pays 10% annually and has risk factor of 0.06.

Type C pays 14% annually and has risk factor of 0.10.

So,

Decision Variables are:

[tex]X_{1}[/tex] = Total Amount invested in Type A.

[tex]X_{2}[/tex] = Total Amount invested in Type B.

[tex]X_{3}[/tex] =  Total Amount invested in Type C.

So, the Objective Function will be:

Objective function:

Max Z = 0.08[tex]X_{1}[/tex] + 0.10[tex]X_{2}[/tex]  + 0.14[tex]X_{3}[/tex]

And the Constraints will be:

1. Total Amount Variable:

[tex]X_{1}[/tex] + [tex]X_{2}[/tex]  + [tex]X_{3}[/tex]  [tex]\leq[/tex] 250000

2. Total Risk is no greater than 0.05:

0[tex]X_{1}[/tex]  + 0.06[tex]X_{2}[/tex]  + 0.10[tex]X_{3}[/tex] [tex]\leq[/tex] 0.05

3. At least one fourth of the total amount invested to be allocated to Type A investment.

[tex]X_{1}[/tex] [tex]\geq[/tex] 0.25 ( [tex]X_{1}[/tex] + [tex]X_{2}[/tex]  + [tex]X_{3}[/tex]  )

0.75[tex]X_{1}[/tex]  - 0.25[tex]X_{2}[/tex] - 0.25[tex]X_{3}[/tex] [tex]\geq[/tex] 0

4. At least one fourth of the total amount to be allocated to Type B investment.

[tex]X_{2}[/tex]  [tex]\geq[/tex] 0.25 ( [tex]X_{1}[/tex] + [tex]X_{2}[/tex]  + [tex]X_{3}[/tex]  )

-0.25[tex]X_{1}[/tex]  + 0.75[tex]X_{2}[/tex]  - 0.25[tex]X_{3}[/tex] [tex]\geq[/tex] 0

5. And the non- negativity constraints are:

[tex]X_{1}[/tex],[tex]X_{2}[/tex], and [tex]X_{3}[/tex]  [tex]\geq[/tex] 0

Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.