A company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type A require 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. There are 3 hours and 20 minutes available for cutting and 4 hours
available for assembling. The profit is < 50 each for type A and < 60 each for type B souvenirs. How many
souvenirs of each type should be company manufacture in order to maximuze profit ? Formulate the above
LPP and sovel it graphically and also find the maximum profit.
 

 

 

 

 
 
 
 
 

Answers (1)

Let type A = x          type B = y.
x\geq 0\: ,y\geq 0
 

Item Number  cutting Time Assembly
Time
Profit
Type A x 5 minutes 10 minutes Rs 5
Type B y 8 minute 5 minutes Rs 6
max
Available
Time
  3 hrs 20 min
= 200 min
4 hrs
= 240 min
 

              cutting                                                                    Assembly
Type A requires \rightarrow 5 min                                           Type A requires \rightarrow 10 min
Type B requires\rightarrow 8 min                                            Type B requires \rightarrow 8 min
Max Time = 200 min                                                    Max Time = 240 min
\therefore 5x+8y\leq 200                                                  \therefore 10x+8y\leq 240
x\geq 0,y\geq 0                                                            x\geq 0,y\geq 0
As, we need to maximize the profit
so the function used have will be Maximize
profit on Type A \rightarrow Rs 5
profit on Type B \rightarrow Rs 6
\therefore Maximize Z= 5x+6y
combining all constants
Maximize Z= 5x+6y
subject to constants
5x+8y\geq 200
10x+8y\leq 240 \: \: \: \: x\geq 0,\: y\geq 0
5x+8y\leq 200                                     10x+8y\leq 240
\frac{x}{y} \: \: \frac{40}{0}\: \: \frac{0}{25}                                                \frac{x}{y} \: \: \frac{24}{0}\: \: \frac{0}{30}
corner points                                        value of Z
(0,25)                                                    (150)
(24,0)                                                     120
(8,20)                                                     160 \rightarrow maxi mints
Hence,profit will be maximum if company produces 8 Souvenirs of type A and 20 Souvenirs of Type B
Max profit = Rs 160

                                   

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