Star Oil has $$40$ million available for investment now $($Time $0)$; it estimates that one year from now $($Time $1)$ $$20$ million will be available for investment. Star Oil may purchase any fraction of each investment, but no more than $100\%$ of each opportunity. In this case, the cash outflows and NPV are adjusted accordingly. $\backslash$table$[[$Investments$,1,2,3,4,5],[$Time $0$ cash outflow,$11,53,5,5,29],[$Time $1$ cash outflow,$3,6,5,1,34],[$NPV$,13,16,16,14,39]]$

For example, if Star Oil purchases $1/5$ of Investment $3,$ then a cash outflow of $1/5\backslash$times $5=1$ million dollars would be required at Time $0,$ and a cash outflow of $1/5\backslash$times $5=1$ million would be required at Time $1.$ The $1/5$ share of Investment $3$ would yield an NPV of $1/516=3\mathrm{.}2$ million dollars.

Star Oil wants to maximize the NPV that can be obtained by investing in Investments $15.$ Formulate an LP that will help achieve this goal. Assume that any funds left over at Time $0$ cannot be used at time $1.$

What percentage of Opportunity $3$ should Star Oil invest in$?$