A company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type A require 5 minutes each for cutting and10 minutes each for assembling. Souvenirs of type B require 8 minutes each for cutting and 8 minutes each for assembling. There are 3 hours
20 minutes available for cutting and 4 hours for assembling. The profit for type A souvenirs is Rs 100 each and for type B souvenirs, profit is Rs 120 each. How many souvenirs of each type should the company manufacture in order to maximise the profit ? Formulate the problem as a LPP and then solve it graphically.

 

 

 

 
 
 
 
 

Answers (1)

Let the number of souvenirs of type A and type B be x and y respectively
To maximize : Z= Rs\left ( 100x+120y \right )
subject to constantsx\geq 0,y\geq 0
                                   5x+8y\leq 200
                                   10x+8y\leq 240
corner points                                   value of Z (in Rs)
A(0,25)                                               3000
B(8,20)                                               3200 \leftarrow \: Maximum
C(24,0)                                               2400
Hence the maximum profit of Rs 3200 is obtained when 8 souvenirs of type A and 20 souvenirs of type B is manufactured.

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