Solve these problems using graphical linear programming and answer the questions that follow. Use simultaneous equations to

determine the optimal values of the decision variables.

a$.$ Maximize $,Z=4x_1+3x_2$

Subject to

Material $6x_1+4x_{2}48$ lb

Labor $,4x_1+8x_{2}80$ hour

$x_1,x_{2}0$

What are the optimal values of the decision variables and $Z?$

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

None of the constraints have any slack. Both constraints are binding.

The first constraint has a slack of $10.$

The second constraint has a slack of $15.$

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

None of the constraints have any surplus.

The first constraint has a surplus of $15.$

The second constraint has a surplus of $20.$