Three cleaning crews are available for a job that requires an area of 1000 square feet to be cleaned. Each cleaning crew charges a fixed cost that is only charged if the company is hired and a variable cost that is dependent on the number of square feet cleaned (see below). The job can be performed either by a single cleaner or by a combination of cleaners. Formulate and solve a mathematical programming model that will determine which crews to hire and how much (in square feet) of the job that each should do.
Company A Cost = 0.01x^2 – 2x + 2000
Company B Cost = 0.005x^2 + x + 4000
Company C Cost = 0.01x^2 – x + 1000