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$10-40$ Cost estimation, cumulative average$-$time learning curve. The WLJ Boat Company, which is under contract to the U$.$S$.$ Navy, assembles troop deployment boats. As part of its research program, it completes the assembly of the first of a new model $($PT$109)$ of deployment boats. The Navy is impressed with the PT$109.$ It requests that WLJ Boat submit a proposal on the cost of producing another six PT$109$s$.$

WLJ Boat reports the following cost information for the first PT$109$ assembled and uses a $90\%$ cumulative average$-$time learning model as a basis for forecasting direct manufacturing labor$-$hours for the next six PT$109$s$.($A $90\%$ learning curve means $b=-0\mathrm{.}152004.)$

"Using the formula $($page $384)$ for a $90\%$ learning curve, $b=\frac{ln0\mathrm{.}90}{ln2}=\frac{-0\mathrm{.}105361}{0\mathrm{.}693147}=-0\mathrm{.}152004$

${?}^b$ Tooling can be reused at no extra cost because all of its cost has been assigned to the first deployment boat.

$\backslash$table$[[$Direct materials cost,$$205,000$ per PT$109],[$Direct manufacturing labor time for first boat,$15,200$ direct manufacturing labor$-$hours$],[$Learning curve for manufacturing labor time per boat,$90\%$ cumulative average time ${?}^a$