In a contract for three more units, how many labor hours should Simpson plan for? $($Answer in Appendix E$)$

$6.$ Lazer Technologies Inc. $($LTI$)$ has produced a total of $20$ high$-$power laser systems that could be used to destroy any approaching enemy missiles or aircraft. The $20$ units have been produced, funded in part as private research within the research and development arm of LTI, but the bulk of the funding came from a contract with the U$.$S$.$ Department of Defense $($DoD$).$

Testing of the laser units has shown that they are effective defense weapons, and if redesigned to add portability and easier field maintenance, the units could be truck$-$mounted.

The DoD has asked LTI to submit a bid for $100$ units.

The $20$ units that LTI has built so far cost the following amounts and are listed in the order in which they were produced.

$\backslash$table$[[$Unit Number,Cost millions$),$Unit Number,Cost millions$)],[1,$$$12,11,3\mathrm{.}9],[2,10,12,3\mathrm{.}5],[3,6,13,3\mathrm{.}0],[4,6\mathrm{.}5,14,2\mathrm{.}8],[5,5\mathrm{.}8,15,2\mathrm{.}7],[6,6,16,2\mathrm{.}7],[7,5,17,2\mathrm{.}3],[8,3\mathrm{.}6,18,3\mathrm{.}0],[9,3\mathrm{.}6,19,2\mathrm{.}9],[10,4\mathrm{.}1,20,2\mathrm{.}6]]$

a$.$ Based on past experience, what is the learning rate?

b$.$ What bid should LTI submit for the total order of $100$ units, assuming that learning continues?

c$.$ What is the cost expected to be for the last unit under the learning rate you estimated?

$7.$ Johnson Industries received a contract to develop and produce four high$-$intensity long$-$distance receiver$/$transmitters for cellular telephones. The first took $2,000$ labor hours and $$39,000$ worth