A company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type A requires 5 minutes each for cutting and 10 minutes each for assembling. Souvenirs of type B require 8 minutes each for cutting and 8 minutes each for assembling. Given that total time for cutting is 3 hours 20 minutes and for assembling 4 hours. The profit for type A souvenir is rupees 100 each and for type B souvenir, profit is rupees 120 each. How many souvenirs of each type should the company manufacture in order to maximize the profit ? Formulate the problem as an LPP and solve it graphically.

 

 
 
 
 
 

Answers (1)

\\$ Let the company manufacture $ x$ number of souvenirs of Type $\mathrm{A}$ and $y$ number of souvenirs of Type B

\\ \text { According to the question } \\ 5 x+8 y \leq 200 \\ 10 x+8 y \leq 240 \\ x \geq 0, y \geq 0

\text { Maximise the profit } P=100 x+120 y

The common area is coverd by point OABC.

Point A (0,25) , B(8,20), C(24,0)

\\ $Check at corner points $ \\ \mathrm{P}(\mathrm{A})= $ Rs 3,000$ \\ \mathrm{P}(\mathrm{B})= $ Rs 3,200(\text { Maximum profit })$ \\ \mathrm{P}(\mathrm{C})= $ Rs 2,400

\\$ For Maximum profit the number of souvenirs of Type A is 8 and Type \mathrm{B} is 20

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