Alex can choose from five investment opportunities. Their respective costs and expected returns are summarized below: Expected
Question:
Alex can choose from five investment opportunities. Their respective costs and expected returns are summarized below:
Expected Return | Cost | |
Opportunity 1 | $16,000 | $5,000 |
Opportunity 2 | $22,000 | $7,000 |
Opportunity 3 | $12,000 | $4,000 |
Opportunity 4 | $21,000 | $6,000 |
Opportunity 5 | $8,000 | $3,000 |
Note that partial investment is not allowed. Multiple units of the same investment opportunity are not allowed, either. At present, Alex has $17,000 available funds for investment. Build an integer program to maximize Alex's total expected return, subject to the following constraints:
a) Alex must invest in at least two opportunities.
b) If Alex invests in Opportunity 2, he also must invest in Opportunity 1.
Part (A) Writing your math model on a piece of paper:
- Define the decision variables. (5 points)
- What is the objective function? (5 points)
- What are the constraints? (9 points)
Part (B) Using Excel to implement your math model. After using the Solver, answer the following questions:
- Use one Excel worksheet to show your solution (5 points).
- What's the optimal expected return? Please type your answers in your Excel file. (4 points)
- Which opportunities should Alex choose? Please type your answers in your Excel file. (3 points)
Opportunity 1 and Opportunity 2 are in the Energy industry while Opportunity 3, Opportunity 4, and Opportunity 5 are in the Healthcare industry. Keep the original two constraints, i.e., Constraints a) and b)) and add the following two new constraints.
c) No more than one opportunity can be picked from the Energy industry.
d) At least one opportunity must be picked from the Healthcare industry.
Part (C) Writing your math model on a piece of paper:
- What are the new constraints? (6 points)
Part (D) Using Excel Solver to show:
- Use another Excel worksheet to show your solution. (5 points)
- What is the new optimal expected return? Please type your answers in your Excel file. (2 points)
- Which opportunities should Alex choose? Please type your answers in your Excel file. (3 points)?
Keep the original two constraints, i.e. Constraints a) and b). Ignore the two constraints, i.e., Constraints c) and d). Add the following new constraint:
e) Alex does not want to buy Opportunity 1 and Opportunity 3 at the same time.
Part (E) Writing your math model on a piece of paper:
- What is the new constraint? (3 points)
Part (F) Using Excel Solver to show:
- Use another Excel worksheet to show your solution. (5 points).
- What is the new optimal expected return? (2 point)
- Which opportunities should Alex choose (3 points)? Answer it
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill