2. 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. For each alternative machine type, write the equations for (i) Total cost, (ii) Total Revenue and (iii) Profit-as a function of the number of more carpet cleaning demand (Q). a) b) Machine B needs to clean how many more carpets than machine A to break even? Plot the Profit graphs (on same graph) for each machine type. From your graph, recommend over what range of more carpet cleaning demand (Q) will which machine type be preferred. c)