Question: A Set up the linear programming problem that a benefits

A. Set up the linear programming problem that a benefits officer might use to determine the total-return maximizing allocation of the employee's pension portfolio. Use the inequality forms of the constraint conditions.
B. Solve this linear programming problem and interpret all solution values. Also determine the employee's expected before-tax and after-tax income levels.
C. Calculate the amount of unrealized capital gain earned per year on this investment portfolio.
D. What is the total return opportunity cost of the $6,000 after-tax income constraint?
Several companies have learned that a well-funded and comprehensive employee benefits package constitutes an important part of the compensation plan needed to attract and retain key personnel. An employee stock ownership plan, profit-sharing arrangements, and deferred compensation to fund employee retirement are all used to allow productive employees to share in the firm's growth and development. Among the fringe benefits offered under the cafeteria-style benefits plans is comprehensive medical and dental care furnished through local health maintenance organizations, on-site daycare centers for employee children, and "eldercare" support for the aging parents and other dependents of workers.
Many companies also provide their employees with so-called "defined benefit" pension plans. Under defined benefit plans, employers usually offer workers a fixed percentage of their final salary as a retirement annuity. In a typical arrangement, a company might offer employees a retirement annuity of 1.5 percent of their final salary for each year employed. A 10-year veteran would earn a retirement annuity of 15 percent of final salary, a 20-year veteran would earn a retirement annuity of 30 percent of final salary, and so on. Because each employee's retirement benefits are defined by the company, the company itself is obligated to pay for promised benefits.

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