d . What is the marginal value ( shadow price ) of machine time? e . What impact would decreasing labor by 30 have on

d$.$ What is the marginal value $($shadow price$)$ of machine time? e$.$ What impact would decreasing labor by $\mathrm{30}$ have on overall profit? A garden store prepares various grades of pine bark for mulch: nuggets, mini$-$nuggets, and chips, with profits of $\backslash (\backslash$$ $\mathrm{5.50},\backslash$$ $\mathrm{4.25}\backslash ),$ and $\backslash (\backslash$$ $\mathrm{6.75}\backslash )$ per bag respectively. The mulching process requires pine bark $(\mathrm{400}$ pounds available$),$ machine time $(\mathrm{440}$ minutes available$),$ labor time $(\mathrm{475}$ minutes available$).$ Each bag of nuggets requires $2$ pounds of bark, $2$ minutes of machine time and $3$ minutes of labor. Each bag of mini$-$nuggets requires $\mathrm{2.5}$ pounds of bark, $1$ minutes of machine time and $2$ minutes of labor. Each bag of chips requires $3$ pounds of bark, $2$ minutes of machine time and $1$ minutes of labor. The garden store is committed to producing at least $\mathrm{30}$ bags of chips, and $\mathrm{40}$ bags of mini$-$nuggets. a$.$ How many bags of each type of mulch should be made to maximize profit? Nuggets $\backslash (=\backslash ),$ mini$-$nuggets $\backslash (=\backslash ),$ chips $\backslash (=\backslash )$ b$.$ What is the optimal profit? c$.$ For this solution, what is the marginal value $($shadow price$)$ of a pound of pine bark?