Math, asked by Mehmoodkhanmeerzai55, 2 months ago

A petroleum refinery sells two products petrol and fuel oil. Net profit

from petrol is Rs. 160 per barrel and fuel oil is Rs. 80 per barrel. There are two

constraints storage capacity is limited to 5000 gallons for petrol and 12000 gallons

for fuel oil. The refining plant has a maximum capacity of 27000 units. Each gallon

of petrol requires 3 units of refining capacity and each gallon of fuel oil requires 2

units.

(a): Formulate the LP problem.

Answers

Answered by amitnrw

1

Given : A petroleum refinery sells two products petrol and fuel oil. Net profit from petrol is Rs. 160 per barrel and fuel oil is Rs. 80 per barrel. There are two constraints storage capacity is limited to 5000 gallons for petrol and 12000 gallons for fuel oil. The refining plant has a maximum capacity of 27000 units. Each gallon of petrol requires 3 units of refining capacity and each gallon of fuel oil requires 2 units.

To Find : Formulate the LP problem.

Solution:

X = unit of Petrol

Y = unit of Fuel oil

X ≤ 5000

Y ≤ 12000

3X + 2Y ≤ 27000

Z = 160X + 80Y Z is Profit

points on boundary

( 5000 , 0) , ( 5000 , 6000) , ( 1000 , 12000) , (0 , 12000)

Z = 160X + 80Y

X Y Z = 160X + 80Y

5000 0 800000

5000 6000 1400000

1000 12000 1120000

0 12000 960000

Maximum profit at , ( 5000 , 6000)

Petrol = 5000 unit

Fuel oil = 6000 unit

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