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 each for type A and 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.
Let type A = x type B = y.
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 5 min Type A requires 10 min
Type B requires 8 min Type B requires 8 min
Max Time = 200 min Max Time = 240 min
As, we need to maximize the profit
so the function used have will be Maximize
profit on Type A Rs 5
profit on Type B Rs 6
Maximize
combining all constants
Maximize
subject to constants
corner points value of Z
(0,25) (150)
(24,0) 120
(8,20) 160 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