FINANCIAL INVESTMENT. The Investment Club at Bell Labs has solicited and obtained $50,000 from its members. Collectively, the members have selected the three stocks, two bond funds, and a tax-deferred annuity shown in the following table as possible investments.
The club members have decided on the following strategies for investment:
• All $50,000 is to be invested.
• At least $10,000 is to be invested in the tax-deferred annuity.
• At least 25% of the funds invested in stocks are to be in the low-risk stock (TAT).
• At least as much is to be invested in bonds as stocks.
• No more than $12,500 of the total investment is to be placed in investments with projected annual returns of less than 10%.
a. Formulate and solve a linear program that will maximize the total projected annual return subject to the conditions set forth by the Investment Club members.
b. What is the projected rate of return of this portfolio? What rate of return should investors expect on any additional funds received, given the restrictions of the club? Explain why this rate would hold for all additional investment dollars.
c. For which investment possibilities are the estimates for the projected annual return most sensitive in determining the optimal solution?
d. Give an interpretation of the shadow prices for the right-hand side of each constraint.