Working out the cost of labour.

Question

A contractor is appointed to paint a house. He wants to keep his labour costs as low as possible. It costs R200 for each painter (x) and a further R20/hour for each painter. He has determined that it would take one person 100 hours to finish the work alone. Presume it is going to take (y) hours to complete the job and that all painters are equally efficient.

 

The contractor decides (without any calculations) that the best would be to appoint three painters. What will his total labour cost be?

Answer 1

Let's start by thinking about the 100 hours it will take to finish the work, ignoring the flat cost of R200 for each painter.

 

The problem says that one person would finish the work in 100 hours, which means the contractor would wind up paying him 100×R20 = R2000 for his work. If the contractor hired two people, they would each work 50 hours, which means the contractor would pay each of them 50×R20 = R1000, for a total of R2000. Four people would work 25 hours each and cost 25×R20 = R500 each, for a total of R2000 again. So, no matter how many painters are hired, the contractor will have to pay R2000 total for the 100 hours of work.

 

Since the contractor will always pay R2000 plus an additional R200 for each painter, you can write an equation for the amount the contractor will have to pay (P), where x is the number of painters:

 

P = R200x + R2000

 

Using that equation, you can figure out how much money three painters will cost by plugging in x=3.