unit. Probability distributions for the purchase cost, the labor cost, and the transportation cost are estimated in the following table.

$\backslash$table$[[\backslash$table$[[$Procurement$],[$Cost$($$$)]],$Probability,$\backslash$table$[[$Labor$],[$Cost $($$$)]],$Probability,$\backslash$table$[[$Transportation$],[$Cost $($$$)]],$Probability$],[10,0\mathrm{.}25,20,0\mathrm{.}10,3,0\mathrm{.}75],[11,0\mathrm{.}45,22,0\mathrm{.}25,5,0\mathrm{.}25],[12,0\mathrm{.}30,24,0\mathrm{.}35,,]]$

$($a$)$ Compute profit $($in $$)$ per unit for the base$-$case scenario.

$$,\frac{?}{\text{u}\text{n}\text{i}\text{t}}$

$($b$)$ Compute profit $($in $$)$ per unit for the worst$-$case scenario.

$ $\frac{?}{\text{u}\text{n}\text{i}\text{t}}$

$($c$)$ Compute profit $($in $$)$ per unit for the best$-$case scenario.

$$,\frac{?}{\text{u}\text{n}\text{i}\text{t}}$

$($d$)$ Construct a simulation model to estimate the mean profit $($in $$)$ per unit. $($Use at least $1,000$ trials. Round your answer to two decimal places.$)$ $

$($e$)$ Why is the simulation approach to risk analysis preferable to generating a variety of what$-$if scenarios?

Simulation will provide of the profit per unit values which can then be used to find of an unacceptably low profit. $($Round your answer to three decimal places.$)$