A linear programming computer package is needed.

here.

percentage of cherry cabinets assigned to cabinetmaker $2,$ and $C3=$ percentage of cherry cabinets assigned to cabinetmaker $3.)$

Min

s$.$t$.$

hours available $1$

hours available $2$

hours available $3$

oak

cherry

$O1,O2,O3,C1,C2,C30$

place.$)$

$($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 $26\mathrm{.}458$ hours, so increasing cabinetmaker $1\text{'}$s time will not reduce costs.

No$,$ cabinetmaker $1$ has a slack of $37\mathrm{.}5$ 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 $26\mathrm{.}458$ hours, so increasing cabinetmaker $2\text{'}$s time will not reduce costs.

No$,$ cabinetmaker $2$ has a slack of $37\mathrm{.}5$ 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 $O2$ and $C2$ are