Bob's candle factory is considering three different manufacturing options. Option A uses hand labor with an intitial cost of $$10,000$ and material costs of $$\frac{2\mathrm{.}75}{?}$ candle. Option B uses combination of hand and automation with an initial cost of $$12,000$ and material costs of $$\frac{1\mathrm{.}10}{?}$ candle. Option C is highly automated with an initial cost of $$15,000$ and material costs of $$\frac{0\mathrm{.}75}{?}$ candle.

a$.$ What are the crossover points? A$[$Blank$1]$; B$[$Blank$2]$; C$[$Blank$3]$

b$.$ At what output does Option B become less expensive than Option A$?[$Blank$4]$

c$.$ At what output does Option C become less expensive than Option B$?[$Blank$5]$

d$.$ If the forecasted demand for candles is $2,800$ units, which option should Bob Candles's choose? $[$Blank$6],$ and what is the cost? $[$Blank$7]$