$4.(40$ points$)$ Upon graduation, you started your own investment company and received $\backslash (\backslash$$ $1,000,000\backslash )$ from an investor who chose to trust you based on the University of Florida being ranked $\backslash (7^\{\backslash$text $\{$th $\}\}\backslash )$ among public schools in the United States, where you graduated from its business school. The investor's goal is to maximize their return over a one$-$year period.

To achieve this, you have decided to invest in Exchange$-$Traded Funds $($ETFs$)$ across various industries. However, you want to ensure that the investment strategy is not overly risky. To mitigate risk, you have set the following constraints:

i$)$ Invest at least $\backslash (8\backslash \%\backslash )$ of the total investment $\backslash ((\backslash$$ $1,000,000)\backslash )$ in each selected ETF $($see table in the following page$)$ and no more than $\backslash (20\backslash \%\backslash )$ of the total investment in a single ETF.

ii$)$ Invest at least $\backslash (10\backslash \%\backslash )$ of the total investment in U$.$S$.$ Treasury Bill $($GB$12$:Gov$)$ to provide a safe and stable return. There is no upper limit on how much you can invest in GB$12$:Gov.

iii$)$ Average Risk should be no more than $0\mathrm{.}65.$

a$)$ Given these constraints, how would you allocate the $\backslash (\backslash$$ $1,000,000\backslash )$ across the available ETFs and U$.$S$.$ Treasury Bill to achieve the maximum return while meeting the diversification and safety requirements? $(20$ Points$)$

b$)$ What is the expected return after $1$ year? What is the average risk? $(5$ Points$)$

c$)$ Which constraints are not binding? $(5$ Points$)$

d$)$ Assume you are considering one of the following two options:

Option $1$: The constraint for investing in U$.$S$.$ Treasury Bill is relaxed. That is$,$ you can choose not to invest any amount in U$.$S Treasury Bills. All other constraints remain the same. You are still allowed to invest in Treasury Bills.

Option $2$: The constraint for investing in IWM is relaxed. That is$,$ you can choose not to invest any amount in IWM. All other constraints remain the same. You are still allowed to invest in IWM.

Which one would you choose? Why? $(10$ Points$)$