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# Investing In Stocks: Oil Alaska and Southwest Petroleum

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Financial Analysts, an investment firm, manages stock portfolios. The firm is considering investing in two stocks for a particular client. The client has a total of \$60,000 to invest. Oil Alaska shares cost \$30 per share. Southwest Petroleum shares cost \$40 per share. Oil Alaska returns \$6 per share per year and Southwest Petroleum returns \$5 per share per year. Which of the following statements is true about Financial Analysts' portfolio optimization problem? (Assume X1 = Oil Alaska shares and X2 = Southwest Petroleum shares).

A. The objective function minimizes 30X1 + 40X2

B. The objective function maximizes 30X1 + 40X2

C. 30X1 + 40X2 ? 60,000 is a constraint of the problem

D. 6X1 + 5X2 ? 60,000 is a constraint of the problem

#### Solution Preview

Dear Student:

Assuming that X1 = number of Oil Alaska selling at \$30 per share and X2 = number of Southwest Petroleum selling at \$40 per share, we find the total dollar amount of the client?s investment using the following formula:

Total Investment in dollars = 30X1 + 40X2
Maximum investment that ...

#### Solution Summary

The expert examines investing in stocks for Oil Alaska and Southwest Petroleum. The objective function maximizes are determined.

\$2.19

## Setting up an investment optimization problem

Financial Analysts, Inc. is an investment firm that manages stock portfolios for a number of clients. A new client has just requested that the firm handle an \$80,000 portfolio. As an initial investment strategy the client would like to restrict the portfolio to a mix of the following two stocks:

Price/share: \$50
Estimates annual return/share: \$6
Maximum possible investment: \$50,000

Stock: Southwest Petroleum
Price/share: \$30
Estimates annual return/share: \$4
Maximum possible investment: \$45,000

Let x = number of shares of Oil Alaska and y = number of shares of Southwest Petroleum

Part A: Develop the objective function, assuming that the client desires to maximize the total annual return
Part B: Show the mathematical expression for each of the following three constraints:
1. Total investment funds available are \$80,000
2. Maximum Oil Alaska investment is \$50,000
3. Maximum Southwest Petroleum investment is \$45,000

Note: this problem only sets up the problem. It does not solve for x and y.

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