IDNLearn.com makes it easy to get reliable answers from knowledgeable individuals. Discover in-depth and trustworthy answers from our extensive network of knowledgeable professionals.
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
Your presence in our community is highly appreciated. Keep sharing your insights and solutions. Together, we can build a rich and valuable knowledge resource for everyone. IDNLearn.com provides the answers you need. Thank you for visiting, and see you next time for more valuable insights.
