A petroleum company has three plants. From a barrel of crude oil, factory #1 can

ID: 3109583 • Letter: A

Question

A petroleum company has three plants. From a barrel of crude oil, factory #1 can produce 20 gallons of motor oil, 10 gallons of diesel oil and 5 gallons of gasoline. There is also waste in the form of paraffin, among other things. Similarly, factory #2 can produce 4 gallons, 14 gallons, and 5 gallons, respectively, while factory #3 can produce 4 gallons,5 gallons, and 12 gallons, respectively of motor, diesel, and gasoline. Factory #1 has 3 gallons of paraffin to dispose of per barrel crude, factory #2 5 gallons, and factory #3 2 gallons. The current daily demand from distributors is 5000 gallons of motor oil, 8500 gallons of diesel oil and 10000 of gasoline. Set up the system of equations which describes the above situation. Next, decide how many barrels of crude oil each plant should get in order to meet the as a group. Remember that you can only provide each plant with an integer number of barrels.

Explanation / Answer

a). From the given specifications, we can set up a system of equations to represent the output of the factories:

Motor Oil: 20f1 + 4f2 + 4f3 = x1

Diesel Oil: 10f1 + 14f2 + 5f3 = x2

Gasoline: 5f1 + 5f2 + 12f3 = x3

Where f1, f2 , and f3 are the number of barrels of oil provided to each factory, and x1 , x2 , and x3 are the outputs of each product, respectively. We can then use these equations to find the amount of oil to give to each factory to meet a given demand.

b). The first demand to meet is 5000 gallons of motor oil, 8500 gallons of diesel oil, and 10000 gallons of gasoline. Solving the system of equations gives us the input for each factory in barrels of oil, as shown in the table below:

Factory 1

Factory 2

Factory 3

Demand / Total Barrel

Motor oil

5000

Diesel oil

8500

Gasoline

10000

Paraffin

Barrels of oil (Exact)

48.75

331.25

675.00

1055

Barrels of oil (Approximate)

332

675

1056

Barrels of oil are obtained by solving the three equations by replacing x1, x2 and x3 with the demands 5000, 8500 and 10000 respectively.