An automobile manufacturer makes automobiles and trucks in a factory that is divided
into two shops. Shop A, which performs the basic assembly operation, must work 5
man-days on each truck but only 2 man-days on each automobile. Shop B, which
performs finishing operations, must work 3 man-days for each automobile or truck
that it produces. Because of men and machine limitations, shop A has 180 days mandays per week available while Shop B has 135 man-days per week. If the manufacturer
makes a profit of rupees 30000 on each truck and rupees 2,000 on each automobile,
how many of each should be produced to maximize his profit? formulate this as LPP
and solve the problem.
Answers
Given : An automobile manufacturer makes automobiles and trucks in a factory
To Find : how many of each should be produced to maximize his profit? formulate this as LPP
Solution:
Truck = X
Automobile = Y
X , Y ≥ 0
5X + 2Y ≤ 180
3X + 3Y ≤ 135
=> X + Y ≤ 45
Points are
(36 , 0)
(30 , 15)
(0 , 45)
Profit = 30000X + 2000Y
X Y Profit
36 0 1080000
30 15 930000
0 45 90000
so Max profit if only 36 Trucks are manufactured
if Profit is 3000X + 2000Y
X Y Profit
36 0 108000
30 15 120000
0 45 90000
Then Max profit is when Truck = 30 and Automobile = 15
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