An international graduate student will receive a $ 28,000 foundation scholarship and reduced tuition. She must pay $ 1,500 in tuition for each of the autumn, winter, and spring quarters, and $ 500 in the summer. Payments are due on the first day of September, December, March, and May, respectively. Living expenses are estimated to be $ 1,500 per month, payable on the first day of the month. The foundation will pay her $ 18,000 on August 1 and the remainder on May 1. To earn as much interest as possible, the student wishes to invest the money. Three types of investments are available at her bank: a 3 month CD, earning 0.75% ( net 3 month rate); a 6 month CD, earning 1.9%; and a 12 month CD, earning 4.2%. Develop a linear optimization model to determine how she can best invest the money and meet her financial obligations.