Reconsider the Welte Mutual Funds problem from Section 9.2. Define your decision variables as the fraction of funds invested in each security. Also, modify the constraints limiting investments in the oil and steel industries as follows: No more than 50% of the total funds invested in stock (oil and steel) may be invested in the oil industry, and no more than 50% of the funds invested in stock (oil and steel) may be invested in the steel industry.

a. Solve the revised linear programming model. What fraction of the portfolio should be invested in each type of security?

b. How much should be invested in each type of security?

c. What are the total earnings for the portfolio?

d. What is the marginal rate of return on the portfolio? That is, how much more could be earned by investing one more dollar in the portfolio?

PLEASE USE EXCEL SOLVER AND SHOW STEPS

reference question

Consider the case of Welte Mutual Funds, Inc., located in New York City. Welte just obtained $100,000 by converting industrial bonds to cash and is now looking for other investment opportunities for these funds. Based on Weltes current investments, the firms top financial analyst recommends that all new investments be made in the oil industry, in the steel industry, or in government bonds. Specifically, the analyst identified five investment opportunities and projected their annual rates of return. The investments and rates of return are shown in Table 9.3. Management of Welte imposed the following investment guidelines:

1. Neither industry (oil or steel) should receive more than $50,000.

2. Government bonds should be at least 25% of the steel industry investments.

3. The investment in Pacific Oil, the high-return but high-risk investment, cannot be more than 60% of the total oil industry investment. What portfolio recommendationsinvestments and amountsshould be made for the available $100,000? Given the objective of maximizing projected return subject to the budgetary and managerially imposed constraints, we can answer this question by formulating and solving a linear programming model of the problem. The solution will provide investment recommendations for the management of Welte Mutual Funds

investment OPPORTUNITIES FOR WELTE MUTUAL FUNDS

Investment	Projected rate of return %
Atlantic Oil	7.3
Pacific Oil	10.3
Midwest Steel	6.4
Huber steel	7.5
Government bonds	4.5