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 Septem$-$

ber, December, March, and May, respectively. Living

expenses are estimated to be $$1,500$ per month, pay$-$

able on the first day of the month. The foundation

will pay her $$18,000$ on August $1$ and the remain$-$

der 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 three$-$

month CD$,$ earning $0\mathrm{.}75\%$ at maturity; a six$-$month

$CD,$ earning $1\mathrm{.}9\%$ at maturity; and a $12-$month $CD,$

earning $4\mathrm{.}2\%$ at maturity. Develop a linear optimiza$-$

tion model to determine how she can best invest the

money and meet her financial obligations. $($Please put everything into an excle sheet and use a linear optimziation model for all $3$ types of investments.$)$