c$.$ Maximize

$Z=6A+3B($revenue$)$

Subject to

Material $,20A+6B600lb$

Machinery $25A+20B1,000$ hour

Labor $20A+30B1,200$ hour

$A,B0$

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?

The third constraint has a slack of $120.$

The second constraint has a slack of $60.$

The first constraint has a slack of $80.$

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 second constraint has a surplus of $15.$

The first constraint has a surplus of $20.$

Are any constraints redundant? If yes, which one$($s$)?$

Yes, the first constraint is redundant.

Yes, the second constraint is redundant.

No$,$ there are no redundant constraint.