Martin is evaluating $4$ projects for potential capital funding. However, he only has $$60,000$ for Year one, and $$45,000$ for the remaining years to invest. Unfortunately, he cannot receive any additional funds unspent from year to year. Based on the following data, what is the constraint for the Year $1$ integer programming formulation?

$\backslash$table$[[$Cash Investment,Project $1,$Project $2,$Project $3,$Project$],[$Year $1,50,45,30,40],[$Year $2,10,10,10,10],[$Year $3,10,10,10,10],[$Year $4,0,10,0,10],[$Expected Return,$350,000,400,000,385,000,450,000]]$

Multiple Choice

$={\displaystyle \underset{i=1}{\overset{4}{}}}{a}_{i1}{x}_{i}60,000$

$={\displaystyle \underset{i=1}{\overset{4}{}}}{a}_i{x}_{i}45,000$

$={\displaystyle \underset{i=1}{\overset{4}{}}}{a}_{i1}{x}_{i}165,000$