Three cleaning crews are available for a job that requires an area of 1000 squar

Question

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

*Please solve using SOLVER in EXCEL

Explanation / Answer

as we would like to minimize total cost,

hence total cost C =cost of A by cleaing x1 area +cost of B by cleaing x2 area+cost of C by by cleaing x3 area

objective is minimize C

and

cobstraint x1+x2+x3=1000

putting both in excel solver,

Area cleaned by A =337.5

area cleaned by B =375

area cleaned by C =287.5

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