A linear programming computer package is needed.

the cherry cabinets, the number of hours available for the final finishing operation, and the cost per hour to perform the work are shown here.

$67\%,$ of the cherry cabinets if it worked only on cherry cabinets.

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

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

completing both projects? $($Round your percentage values to one decimal 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 $$5$ per hour.

Yes, each additional hour of time for cabinetmaker $1$ will reduce the total cost by $$-1\mathrm{.}75$ 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 $$5$ per hour.

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