Consider that it took a vendor $15,000$ labor$-$hours to produce the first of several aircraft engine components for an aircraft. Your organization has agreed to purchase the tenth $($steady state$)$ aircraft engine component from this vendor to integrate into your modified aircraft. Assume that the vendor experiences a learning rate of $75\%.$ At a labor rate of $$55$ per hour, what should you expect to pay for the tenth unit? Consider your organization pivots and would like to purchase all ten aircraft engine components, how long would it take the vendor to produce all ten aircraft engine components and what would the associated cost be$?\backslash$table$[[$Unit Rate,$70\%,75\%,80\%,85\%],[$Unit Time,Total Time,Unit Time,Total Time,Unit Time,Total Time,Unit Time,Total Time$],[5,\mathrm{.}437,3\mathrm{.}195,\mathrm{.}513,3\mathrm{.}459,\mathrm{.}596,3\mathrm{.}738,\mathrm{.}686,4\mathrm{.}031],[10,\mathrm{.}306,4\mathrm{.}932,\mathrm{.}385,5\mathrm{.}589,\mathrm{.}477,6\mathrm{.}315,\mathrm{.}583,7\mathrm{.}116],[15,\mathrm{.}248,6\mathrm{.}274,\mathrm{.}325,7\mathrm{.}319,\mathrm{.}418,8\mathrm{.}511,530,9\mathrm{.}861],[20,\mathrm{.}214,7\mathrm{.}407,\mathrm{.}288,8\mathrm{.}828,\mathrm{.}381,10\mathrm{.}485,\mathrm{.}495,12\mathrm{.}402],[25,\mathrm{.}191,8\mathrm{.}404,\mathrm{.}263,10\mathrm{.}191,\mathrm{.}355,12\mathrm{.}309,\mathrm{.}470,14\mathrm{.}801],[30,\mathrm{.}174,9\mathrm{.}305,\mathrm{.}244,11\mathrm{.}446,\mathrm{.}335,14\mathrm{.}020,\mathrm{.}450,17\mathrm{.}091],[35,\mathrm{.}160,10\mathrm{.}133,\mathrm{.}229,12\mathrm{.}618,\mathrm{.}318,15\mathrm{.}643,\mathrm{.}434,19\mathrm{.}294],[40,\mathrm{.}150,10\mathrm{.}902,\mathrm{.}216,13\mathrm{.}723,\mathrm{.}305,17\mathrm{.}193,\mathrm{.}421,21\mathrm{.}425]]$

The simplified formula for calculating learning rate time using the table coefficients is given as

where

$=$ time needed to produce the nth unit,

$=$ time needed to produce the first unit, and

$=$ learning curve coefficient. A table of learning curve coefficients is provided below.