Solve these problems using graphical linear programming and then answer the questions that follow. Use simultaneous equations to determine the optimal values of the decision variables.

a$.$ Minimize Z $=1\mathrm{.}80$S $+2\mathrm{.}20$T

Subject to:

Potassium $5$S $+8$T $>=200$ grams

Carbohydrate $15$S $+6$T $>=240$ grams

Protein $4$S $+12$T $>=180$ grams

T T $>=10$ grams

S$,$T $>=0$

Do any constraints have $($nonzero$)$ slack? If yes, which one$($s$)$ and how much slack does each have?

multiple choice $1$

None of the constraints have any slack.

The first constraint has a slack of $10.$

The second constraint has a slack of $15.$