One unit of product A contributes Rs.7: and requires 3 units of raw material and 2 hours
of labour. One unit of product B contributes Rs.5 and requires 1 unit of raw material and
1 hour of labour. Availability of the raw material at present is 48 units and there are 40
hours of labour. Formulate the problem as an LP model to maximize the profit and solve
it graphically,
Answers
Answer:
One unit of produ
ct A contributes Rs.7: and requires 3 units of raw material a
nd 2 hours
of labour. One unit of
r
r
product B contributes Rs.5 and requires 1 unit of raw material and
1 hour of labour.
r
of the raw material at present is 48 units and there are 40
hours of l
abour. Formulate the problem as an LP model to maximize the profit and solve
it graphically,
Given : One unit of product A contributes Rs.7: and requires 3 units of raw material and 2 hours of labour.
One unit of product B contributes Rs.5 and requires 1 unit of raw material and 1 hour of labour.
Availability of the raw material at present is 48 units and there are 40
hours of labour.
To Find :
Formulate the problem as an LP model to maximize the profit and solve
it graphically,
Solution:
unit of product A = x
unit of product B = y
LPP
3x + y ≤ 48
2x + y ≤ 40
z = 7x + 5y
Maximize Z
x , y ≥ 0
as units can not be negative
Draw graph
points from the graph
(16 , 0) , ( 8 , 24) and (0 , 40)
x y z = 7x + 5y
16 0 112
8 24 176
0 40 200
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