Exercise (12.2)
1. A manufacturing company produces two types of batteries low volt and medium volt. A
low volt battery requires 1 hour processing time on machine and 2 hours of labour time.
A medium volt battery requires 2 hours of processing times on machine and 1.5 hours of
labour time. In a week, processing machine is available for 70 hours and labour time
available is 60 hours. The profit due to each of the low volt battery is 60 where as due
to medium volt battery it is *75.
Formulate the problem as L.P.P. with a view to maximise the total profit and solve it
graphically.
Answers
SOLUTION
TO DETERMINE
Formulate the problem as L.P.P. with a view to maximise the total profit and solve it graphically.
EVALUATION
Let x unit of low volt battery and y unit of medium volt battery is produced
Then total machine time = ( x + 2y ) hours
∴ x + 2y ≤ 70 - - - - - - (1)
Total labour time = ( 2x + 1.5y ) hours
∴ 2x + 1.5y ≤ 60
⇒ 4x + 3y ≤ 120 - - - - - - (2)
Profit = 60x + 75y
Hence Converting the given problem in a linear programming problem we get
Maximize z = 60x + 75y
Subject to :
x + 2y ≤ 70
4x + 3y ≤ 120
Where x ≥ 0 and y ≥ 0
Solve graphically :
Graph : Graph is referred to the attachment
We see that OABC is the region bounded by the constraints along with non negativity conditions of the variables
The corner points are
O(0,0) , A (0,35), B(6,32), D(30,0)
For O(0,0) we have z = 0
For A(0,35) we have z = 2625
For B(6,32) we have z = 2760
For C(30,0) we have z = 1800
Thus for z is maximum when x = 6 & y = 32
FINAL ANSWER
The maximum profit is ₹ 2760 when 6 unit of low volt battery and 32 unit of medium volt battery is produced
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