A railway company has to make up its trains of two types of coaches: standard co

Question

A railway company has to make up its trains of two types of coaches: standard coaches which seat 120 people and business coaches which seat 80. The power of the engines unit dictates that no more than ten coaches in total can be pulled, irrespective of their class. Furthermore, under the terms of the rail franchise, each train must be composed of at least 20% but no more than 50% business class coaches. If the average profit per journey for a business class passenger is $40, and for a standard class passenger the figure is $25, what is the maximum profit obtainable per journey?

Explanation / Answer

20%<=business coaches<=50%

total coaches=10 = number of business coaches+ number of standard coaches = Nb+Ns

average profit per journey for a business class passenger = $40

profit from one business coach= 40*80= 3200

average profit per journey for a standard class passenger = $25

profit from one standard coach = 25*120 =3000

maximum profit =?

profit= 40*80*Nb + 25*120*Ns
      = 200( 16Nb + 15Ns )

to maximize profit, business class coach should be maximum .
Hence, Nb=5 (50%)
       Ns=5

max profit=200(16* +15*5) = 1000*31 = $31000

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