Question $4$

Assume you are Project Cost Engineer calculating the cost of the repetitive activities for a project. There are a total of $20$ iterations of this activity required for the project. The project activity takes $2\mathrm{.}5$ hours at its steady state rate and the learning rate is $\backslash (75\backslash \%\backslash ).$

$\backslash [$

Y$\_\{$x$\}=$a X$^\{$b$\}$

$\backslash ]$

Where:

$\backslash ($ Y$\_\{$x$\}=\backslash )$ The time required for steady state, $\backslash ($ x $\backslash ),$ unit of output.

$\backslash ($ a$=\backslash )$ The time required for the initial unit of output.

$\backslash ($ X$=\backslash )$ The number of units to be produced to reach steady state.

$\backslash ($ b$=\backslash )$ The slope of the learning curve, represented as: log decimal learning rate$/$log$2.$

$($a$)$ Explain the idea behind the learning curve concept?

$($b$)$ Calculate the initial output time for the first unit produced using the learning curve formula. $(6$ marks$)$

$($c$)$ Assume the labour cost is $\backslash (\backslash$$ $35\backslash )$ per hour.

$($i$)$ How much you would expect to pay for activity performed in the fifth iteration? $(4$ marks$)$

$($ii$)$ If you have a limited budget of $\backslash (\backslash$$ $120\backslash ),$ does the cost for the $5$ th iteration exceed the budget?

$($iii$)$ What recommendation do you have to mitigate the risk of overspending for the $5$th iteration?