A Research Director Must Pick a Subset of Research Projects $\quad$

A research director must pick a subset of research projects to fund over the next five years. He has five candidate projects, not all of which cover the entire five-year period. Although the director has limited funds in each of the next five years, he can carry over unspent research funds into the next year. Additionally, up to $30K can be carried out of the five-year planning period. The following table summarizes the projects and budget available to the research director.
$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\underline{\text { Project Funds Required (in \( \$ 000 \) )}}$$\quad$$\quad$$\quad$$\text { Benefit}$
$\begin{array}{cccccccc}\text { Project } & 1 & 2 & 3 & 4 & 5 & \text { (in } \$ 000 \text { s) } \\\hline 1 & \$ 70 & \$ 40 & \$ 30 & \$ 15 & \$ 15 & \$ 160 \\2 & \$ 82 & \$ 35 & \$ 20 & \$ 20 & \$ 10 & \$ 190 \\3 & \$ 55 & \$ 10 & \$ 10 & \$ 5 & & \$ 125 \\4 & \$ 69 & \$ 17 & \$ 15 & \$ 12 & \$ 8 & \$ 139 \\5 & \$ 75 & \$ 20 & \$ 25 & \$ 30 & \$ 45 & \$ 174\\\text { Budget } & \$ 225 \mathrm{~K} &\$ 60 \mathrm{~K} & \$ 60 \mathrm{~K} & \$ 50 \mathrm{~K} &\$ 50 \mathrm{~K} \end{array}$
Define the ILP formulation for this capital budgeting problem.