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 $)=(1,2,3$ Build an LP model to maximize the ATK$-$Sugar profit and solve it using the Lindo program. Answer the following questions according to Lindo outputs.

A$)$ If the profit of the first type of candy is $4TL,$ what will be the new best solution?

B$)$ For what profit values of the third type of candy will the current basic solution remain best?

C$)$ If the profit of the third type of candy is $7TL,$ what will be ATKSugar's new best solution?

D$)$ Between what values will the current basic solution remain the best for the amount of sugar the company has?

E$)$ If the company had $70$ units of sugar, what would be its total profit? How many types of candy would the company produce?