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The management of Brinkley Corporation is interested in using simulation to estimate the profit $($in $$)$ per unit for a new product. The selling price for the product will be $$43$ per 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,,],[,,25,0\mathrm{.}30,,]]$

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

$ $/$unit

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

$ $/$unit

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

$ $/$unit

$($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.

$($f$)$ Management believes the project may not be sustainable if the profit per unit is less than $$5.$ Use simulation to estimate the probability the profit per unit will be less than $$5.($Round your answer to three decimal places.$)$