Problem

A junior student earns $20,000 during her summer internship. Since she plans to pursue her graduate study next year, she wants to invest all her earnings in an annual tax saver scheme and non-tax saver plan. The tax saver plan yields a return of 8% with a risk score of 3 and a non-tax saver plan yields 10% with a risk score of 5. To avail the tax exemption, the student has to invest, at least 50% of her investment in a tax saver scheme. A finance professor advises the student to keep the average risk score of the total investment no higher than 3.6. Formulate a linear programming model to maximize the return on investment of the junior's earnings.