$(20$pts$)$ In an attempt by a Contractor $x$ to maximize expected profit when bidding against competitor $Y,$ the following partial computations were done. Let $b$ and $c$ represent the bid and actual cost respectively, while $P_A$ indicate the probability that Contractor $x$ will obtain the bid.

$\backslash$table$[[\frac{b}{c},P_A,$Expected profit $($E$)],[0\mathrm{.}94,1\mathrm{.}00,],[0\mathrm{.}96,0\mathrm{.}98,],[0\mathrm{.}98,0\mathrm{.}97,],[1\mathrm{.}00,0\mathrm{.}96,],[1\mathrm{.}02,0\mathrm{.}93,],[1\mathrm{.}04,0\mathrm{.}81,],[1\mathrm{.}06,0\mathrm{.}78,],[1\mathrm{.}08,0\mathrm{.}69,],[1\mathrm{.}10,0\mathrm{.}45,],[1\mathrm{.}12,0\mathrm{.}12,],[1\mathrm{.}14,0\mathrm{.}05,],[1\mathrm{.}16,0\mathrm{.}02,],[1\mathrm{.}18,0\mathrm{.}00,],[,,]]$

a$.$ Complete the table, sketch the bid strategy plot $($expected profit versus b$/$c$),$ and select the optimum markup $(\%).$

b$.$ The City of Tallahassee has just invited contractors to bid on a building project. Assuming that the only bidders are companies $x$ and $Y,$ and the actual cost of the project is $$2,765,345\mathrm{.}12,$ how much should Contractor $x$ bid? What is the Contractor $x\text{'}$s expected markup$/$profit in dollars?