BMAT 2015 · Question 29 · Optimisation
SaveI want to decorate one of the rooms in my house by painting the four walls. The room is rectangular, measuring 5m by 4m, and is 2.5m high. There is a door in one of the narrower walls, measuring 1m wide by 2m high. There is also a window in the opposite wall to the door, measuring 2m wide by 1.5m high. I do not intend to paint the door or the window. I want to use two different colours, one colour on the two opposing narrower walls and the other colour on the two opposing wider walls. Each colour of paint is available from a high-quality manufacturer at £15 per tin or from a budget manufacturer at £11 per tin. To get a good finish, I need to put two coats of paint on the wall if I am using the high quality paint but three coats if I am using the budget paint. Tins of paint will cover a wall area of 15 square metres in a single coat whichever manufacturer I use. I do not have to use the same quality of paint for the two different colours.
How much do I need to spend on paint in order to achieve a good finish on all four walls without buying any more paint than I have to?