ATK$-$Sugar produces three types of candy with sugar and chocolate. The first type of candy contains $1$ unit of sugar and $2$ units of chocolate. The second type of candy contains $1$ unit of sugar and $3$ units of chocolate. The third type of candy contains $1$ unit each of sugar and chocolate. The profit from candies is $3,6$ and $4$ TL respectively. The company has $50$ units of sugar and $80$ units of chocolate. xi: the amount produced from the ith type of candy