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  • An aeroplane can carry a maximum of 250 passengers. A profit of  Rs1,500 is made on each executive class ticket and a profit of  Rs1,000 is made on each economy class ticket. The airline reserves at least 25 seats for executive class. However

An aeroplane can carry a maximum of 250 passengers. A profit of  Rs1,500 is made on each executive class ticket and a profit of  Rs1,000 is made on each economy class ticket. The airline reserves at least 25 seats for executive class. However, at least 3times as many passengers prefer to travel by economy class than by executive class. Frame the Linear Programming Problem to determine how many tickets of each type must be sold in order to maximize the profit for the airline.

 

 

 

 
 
 
 
 

Answers (1)

Lets assume that excutive class tickets sild be x and economy class be y
\because aeroplane can carry maximum 250 passengers
\therefore x+y\leq 250---(1)
\because  atleast 25 tickets is reserved for excutive class
 \therefore x\geq 25---(2)
Since the number of tickets for economy class should be atleast 3 times the excutive class
\therefore y\geq 3x\Rightarrow y-3x\geq 0---(3)
Also, the number of tickets can't be negative
so x\geq 0\; \S \; y\geq 0---(4)

From equation 1 and equation 3 

x+3x=250

x=62.5

so maximum 62 ticket of executive class can be sell.
Profit on an excutive class tickets is 1500 Rs & profit on an economy class ticket is 1000 Rs
so, Total profit (Z) = 1500x+1000y
corner points                                      value of Z = 1500x +1000y
A(25,225)                                            1500\times 25+1000\times 225= 2,62,500                                     
C(25,75)                                              1500\times 25+1000\times 75= 1,12,500

B(62,188)\\ 1500 \times 62+1000 \times 188=281000

Hence maximum profit will be Rs 281000, when max number of excutive ticket sold be 62 and number of economy class ticket sold be 188.


Posted by

Ravindra Pindel

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