produced, $x_2=$ gallons of Heidelberg Regular produced, and $x_3=$ gallons of Deutschland Extra Dry produced.$)$

$($a$)$ Solve using the simplex method.

$(x_1,x_2,x_3)=(,)$

$($b$)$ What is the value of the slack variable in the Grade A grapes constraint?

Interpret this value.

After reaching the optimal solution, there is still this amount of Grade A grapes to be used.

After reaching the optimal solution, all available Grade A grapes have been used.

In order to reach the optimal solution, this amount of Grade A grapes is required.

What is the value of the slack variable in the Grade B grapes constraint?

Interpret this value.

After reaching the optimal solution, there is still this amount of Grade B grapes to be used.

After reaching the optimal solution, all available Grade B grapes have been used.

In order to reach the optimal solution, this amount of Grade B grapes is required.

What is the value of the slack variable in the sugar constraint?

Interpret this value.

After reaching the optimal solution, there is still this amount of sugar to be used.

After reaching the optimal solution, all available sugar has been used.

In order to reach the optimal solution, this amount of sugar is required.

What is the value of the slack variable in the labor constraint?

Interpret this value.

After reaching the optimal solution, there is still this amount of labor to be used.

After reaching the optimal solution, all available labor has been used.

In order to reach the optimal solution, this amount of labor is required.

$($c$)$ An increase in which resources could improve the company's profit? $($Select all that apply.$)$

Grade A grapes

Grade B grapes

sugar

labor