Northern Defense manufactures radar systems. It has just completed the manufacture of its first newly designed system, RS$-32.$ Manufacturing data for the RS$-32$ follow:

$($Click icon to view more data$)$

Read the requirements.

Requirement $1.$ Calculate the total variable costs of producing $2,3,$ and $4$ units assuming that Northern Defense uses an $85\%$ incremental unit$-$time learning model as a basis for predicting dire manufacturing labor$-$hours.

Begin by calculating the cumulative total time in labor$-$hours using the incremental unit$-$time learning model. $($Round the individual unit time for $x$ th unit to the nearest whole number.$)$

$\backslash$table$[[\backslash$table$[[$Cumulative$],[$number of units$]],\backslash$table$[[$Individual unit time for$],[$Xth unit: Labor$-$hours$]],\backslash$table$[[$Cumulative total time:$],[$Labor$-$hours$]]],[1,,],[2,,],[3,,],[4,,]]$

Data table

Direct materials cost

$ $83,000$ per unit of RS$-32$

Direct manufacturing labor time for first unit

Learning curve for manufacturing labor time per radar system

$3,900$ direct manufacturing labor$-$hours

Direct manufacturing labor costs

$85\%$ incremental unit$-$time ${?}^a$

Variable manufacturing overhead costs

$20$ per direct manufacturing labor$-$hour

$12$ per direct manufacturing labor$-$hour

Using the formula for an $85\%$ learning curve, $b=\frac{ln0\mathrm{.}85}{ln2}=\frac{-0\mathrm{.}162519}{0\mathrm{.}693147}=-0\mathrm{.}234465$