Question

The trains have a maximum length of 11 carriages - this is made up of two engines (one at each end) and between 0 and 9 passenger carriages. Each train will have both first and standard class seating. The train company can decide how many fjirst class carriages it has on the train, but the train length must not be more than 11 carriages long. Each First Class seat generators £8.20 of profit for the train company, while each Standard Class seat only generates £5 of profit. However, there are more seats in a Standard Class carriage than in a First Class one, as is shown in the diagrams below. Each train must have one standard class engine and one first class engine. Each train must be a maximum of 11 cars long, including the two engine cars. Questions a) Calculate the total profit for each different possible combination of First and Standard class passenger and engine carriages. You should also indicate which combination gives the maximum profit. Bi) The 9 passenger carriages are to be painted with advertisements. Two of the carriages will have an identical advert for McDonalds, three will have an identical advert for Kaplan International and the remainder will have identical adverts for The City of Birmingham Symphony Orchestra. Calculate the number of different possible arrangements of these carriages First Class Engine Carriage (18 Seats) Standard Class Carriage (76 seats) Standard Class Engine Carriage (48 seats) First Class Carriage (47 seats) ii) It is decided that the two McDonalds adverts must be combined into one large advert carriages which must cover two adjacent carriages. Taking this into consideration, how many possible arrangements are there now?

Answer 1

Differet combinations annd thaur prt of 1st clars carrager number ofh omdarrd clam cartuages numbun Profit (18X8.2+48 x5) (4-7x8-a)8 (6X 5) + 1 3813 (6) 18x 8.2 3818 4 Crefiet (18x8-2 +48x5)+ 3(43 x2-2)4(36x5) 3893.8 =5 4 4a7x8-9)+5(76xs Prcht =18x8.9 +48x) 3899.9 ,す=4 2= 5 Profit=(18189 4s)+5(41x8-2)(36s) 38 34.6 vi) 1- 6,3 Profpt- 18x8-448xs)4 Ng-2)+(161s) = 3840

(4TH2-9)4 916x5) Profet (18 18 2+48x5)+ 3845-4 viid Crofot-(18n8-2 4tx)+8(47x82) 1 (46x5) y- 1 3850-8 profit it be cbtain for Marumim combination 8 firest clan carua and 1 Atandard clan cauiaye 0). Total pamenger Caouages 9 aduerdiements Goup of 9 3 and 4 total courangemnts 931 41 2 3R9 1260 MeDonalds adverts tro a caruringe l bair grout be cenndered ar So total aurangemenls 8 1 31 4 312 280