(Solved): 30pts) There is a famous puzzle game called "Tents". The game works as follows: In an NN rid, the ...

30pts) There is a famous puzzle game called "Tents". The game works as follows: In an $N\times N$ rid, there are several trees and empty boxes. Moreover, every row and every column are given ith a number, which shows the number of tents in that specific row/column. Also, every tent hould be attached to a tree, and every tree should be attached to a tent. How can we solve the llowing tents problem using integer programming? a) How can we solve the puzzle of $N\times N$ tents? Let $c_j$ denote the number of tents assigned to column $j$, for each $j?\{1,2,\dots ,n\}$ and let $r_i$ denote the number of tents assigned to row $i$, for each $i?\{1,2,\dots ,n\}$. Moreover, we are given a parameter matrix $T$, defined as $T_{ij}=\{\begin{array}{ll}1& \text{ If there is a tree on cell }(i,j),\text{ for each }(i,j)?\{1,2,\dots ,n\}\times \{1,2,\dots ,n\}\\ 0& \text{ Otherwise }\end{array}$ Write an integer programming model using parameters described above. Clearly state your assumptions, decision variables, constraints, objective function, and any other details you deem necessary. (Hint: Do we know how many tents should we place in the optimum solution?)