$($c$)$ If Cabinetmaker $1$ has additional hours available, would the optimal solution change? Explain.

Yes, each additional hour of time for cabinetmaker $1$ will reduce the total cost by $$-1\mathrm{.}75$ per hour.

Yes, each additional hour of time for cabinetmaker $1$ will reduce the total cost by $$5$ per hour.

No$,$ cabinetmaker $1$ has a slack of $37\mathrm{.}5$ hours, so increasing cabinetmaker $1\text{'}$s time will not reduce

costs.

No$,$ cabinetmaker $1$ has a slack of $26\mathrm{.}458$ hours, so increasing cabinetmaker $1\text{'}$s time will not reduce

costs.

$($d$)$ If Cabinetmaker $2$ has additional hours available, would the optimal solution change? Explain.

Yes, each additional hour of time for cabinetmaker $2$ will reduce the total cost by $$-1\mathrm{.}75$ per hour.

Yes, each additional hour of time for cabinetmaker $2$ will reduce the total cost by $$5$ per hour.

No$,$ cabinetmaker $2$ has a slack of $37\mathrm{.}5$ hours, so increasing cabinetmaker $2\text{'}$s time will not reduce

costs.

No$,$ cabinetmaker $2$ has a slack of $26\mathrm{.}458$ hours, so increasing cabinetmaker $2\text{'}$s time will not reduce

costs.

$($e$)$ Suppose Cabinetmaker $2$ reduced its cost to $$38$ per hour. What effect would this change have on the optimal

solution? Explain.

The new objective function coefficients for O$2$ and C$2$ are

respectively. The optimal solution

and has a value of $

and