A linear programming computer package is needed.

$80\%,$ of the oak cabinets if it worked only on oak cabinets. Similarly, Cabinetmaker $1$ can only complete $\frac{40}{60}=0\mathrm{.}67,$ or $67\%,$ of the cherry cabinets if it worked only on 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

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

$($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 O$2$ and C$2$ are

and

$,$ respectively. The optimal solution

$---$Select$---$

and has a value of $

$.$