Min

s$.$t$.$

hours available $2$

hours available $3$

oak

cherry

$\backslash (01,$ O $2,$ O $3,$ C $1,$ C $2,$ C $3\backslash$geq $0\backslash )$

Solve the model formulated in part $($a$).$ What percentage of the oak cabinets and what percentage of the cherry cabinets should be assigned to each cabinetmaker? What is the total cost $($in $\backslash (\backslash$$ $\backslash ))$ of 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 $\backslash (\backslash$$ $5\backslash )$ per hour.

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

Yes, each additional hour of time for cabinetmaker $2$ will reduce the

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

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