Purchase Solution

# Intro to Operations Research Class: Investment Problem

Not what you're looking for?

Al has \$60,000 that he wants to invest now in order to use the accumulation for purchasing a retirement annuity in 5 years. After consulting with his financial adviser, he has been offered four types of fixed-income investments, which we will label as investments A,B,C, D.
Investments A and B are available at the beginning of each of the next 5 years (call them years 1 to 5). Each dollar invested in A at the beginning of a year returns \$1.40 (a profit of \$.40) 2 years later (in time for immediate reinvestment). Each dollar invested in B at the beginning of a year returns \$1.70 three years later.
Investments C and D will each be available at one time in the future. Each dollar invested in C at the beginning of year 2 returns \$1.90 at the end of year 5. Each dollar invested in D at the beginning of year 5 returns \$1.30 at the the end of year 5.
Al wishes to know which investment plan maximizes the amount of money that can be accumulated by the beginning of year 6.

(a) All the functional constraints for this problem can be expressed as equality constraints. To do this let A t, B t, C t, and D t be the beginning of year t for each t where the investment is available and will mature by the end of year 5. Also let R t be the number of available dollars not invested at the beginning of year t (and so available for investment in a later year). Thus, the amount invested at the beginning of year t plus R t must equal the number of dollars available for investment at that time. Write such an equation in terms of the relevant variables above for the beginning of each of the years to obtain the five functional constraints for this problem.
(b)Formulate a complete linear programming model for this problem.

##### Solution Summary

An investment problem is solved using linear programming.

##### Solution Preview

As investment 'A' matures every 2 yrs, therefore investments in `A' will be: A1, A2, A3, A4 at the beginning of years 1,2,3 and 4 respectively and the returns will be 1.4A1, 1.4A2, 1.4A3 and 1.4A4 at thends of year 2, 3, 4 and 5 respectively.

Invsetment B: matures after 3 yrs.
Therefore investments will be: B1, B2, B3 at the beginning of years 1, 2 and 3 respectively and returns will be 1.7B1, 1.7B2 and 1.7B3 at the ends of years ...

Solution provided by:
###### Education
• MSc , Pune University, India
• PhD (IP), Pune University, India
###### Recent Feedback
• " In question 2, you incorrectly add in the \$3.00 dividend that was just paid to determine the value of the stock price using the dividend discount model. In question 4 response, it should have also been recognized that dividend discount models are not useful if any of the parameters used in the model are inaccurate. "
• "feedback: fail to recognize the operating cash flow will not begin until the end of year 3."
• "Great thanks"
• "Perfect solution..thank you"

##### Free BrainMass Quizzes

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

##### Probability Quiz

Some questions on probability

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.