$[$USE EXCEL$]$Gallant Carpet Cleaning cannot meet demand with its current equipment. Gallant Carpet Cleaning is considering two new carpet cleaning machines. Machine A cleans carpets to residential standards, while machine B cleans and sanitizes carpets to hospital standards. Machine A costs $$20,000$ and machine B costs $$50,000.$ The company estimates its cost per cleaning $($including all chemicals$)$ for machine A will be $$8$ and machine B will be $$7.$ The revenue per carpet cleaned for A would be $$40,$ while B could bring in $$45$ per carpet, due to the higher degree of sanitation provided.

a$.$ Complete the table below for the data as well as equations $($using Q $)$ for Total cost $($TC$),$ Total Revenue $($TR$)$ and Profit $($Pr$).$

$\backslash$table$[[\backslash$table$[[$# of$],[$Carpets$],[$cleaned$],[$Q$]],$Machine A$,$Machine B$],[$FC$,20000,],[\backslash$table$[[$v Variable$],[$cos$1/$unit$]],8,50000],[$Selling price,,$],[=R,,]]$

b$.$ Machine B needs to clean how many more carpets than machine A to break even?

c$.$ Plot the Profit graphs $($on same graph$)$ for each machine type. From your graph, recommend over what range of more carpet cleaning demand $(Q)$ which machine type will be preferred.