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PROJECT #2 Petroleum Industry Management Tasha Mayo Cary Smith Kristi Stewart SYSTEM OF EQUATIONS Factory 1: 20(M) + 10 (D) + 5 (G) + 3 (P) Factory 2: 4 (M) + 14 (D) + 5 (G) + 5 (P) Factory 3: 4 (M) + 5 (D) + 12(G) + 2 (P) We need to find 3 scalars, a, b & c such that:

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project 2 petroleum industry management

PROJECT #2 Petroleum Industry Management

Tasha MayoCary SmithKristi Stewart

system of equations
SYSTEM OF EQUATIONS

Factory 1: 20(M) + 10 (D) + 5 (G) + 3 (P)

Factory 2: 4 (M) + 14 (D) + 5 (G) + 5 (P)

Factory 3: 4 (M) + 5 (D) + 12(G) + 2 (P)

We need to find 3 scalars, a, b & c such that:

a(F1) + b(F2) + c(F3) = Demand

Current demand is:

5000 (M) + 8500 (D) + 10000 (G)

**under current demand, Paraffin is not needed, so we will not consider it in our initial matrix

calculations
CALCULATIONS

a(F1) + b(F2) + c(F3) = Demand

REDUCES TO:

evaluate
EVALUATE

We must now find

a, b & c as using the

following equations:

5a + b + c = 1250

4b +11c = 8750

c = 675

Using back substitution, we get:

4b + 11(675) = 8750

4b + 7425 = 8750

4b = 8750

b = 331.25

5a + 331.25 + 675 = 1250

5a = 243.75

a = 48.75

barrel disbursement
BARREL DISBURSEMENT

Since we cannot allot partial barrels, it is necessary to round up to the next whole number. The following production will meet current daily demand:

a(F1) + b(F2) + c(F3) = 5000(M) + 8500(D) + 10000(G)

F1: 49(20M + 10D + 5G) = 980M + 490D + 245G

F2: 332(4M + 14D + 5G) = 1328M + 4648D + 1660G

F3: 675(4M + 5D + 12G)= 2700M + 3375D + 8100G

5008M + 8513D +10005G

demand doubled
DEMAND DOUBLED

Reduces to:

Using back substitution, we find values:

a = 97.5, b = 662.5, and c = 1350

These values are approximately double those we found for the original demand.

5a + b + c = 2500

4b + 11c = 17500

c = 1350

new distributors
NEW DISTRIBUTORS

REDUCES TO:

5a + b + c = 500

4b + c = 1000

c = 250

Using back substitution, we get these values:

a = 12.5, b = 187.5, c = 250

If we add the demand of this new distributor to our current daily demand, we find new values for a, b and c:

a = 61.25, b = 518.75, and c = 925

Notice that this is roughly equal to the number of barrels for each demand (per factory) added together.

sensitivity analysis
SENSITIVITY ANALYSIS
  • - 3% change in demand for gasoline:

Gives the following values: a = 53.25 (+ 9.2% change)

b = 338.75 (+ 2.3% change)

c = 655 (-3% change)

  • +3% change in demand for gasoline:

Gives the following values: a = 44.25 (-9.2% change)

b = 323.75 (-2.3% change)

c = 705 (+ 4.4% change)

These values do not fluctuate much, and production is still easily met for slight changes in demand.

plant off line
PLANT OFF LINE
  • Set up augmented matrix with just F1 and F2
  • Reduce
  • We find a system of equations that imply 0=3375, which is not possible.
  • Current daily demand for all products cannot be met
  • Suggest meeting demand for motor oil and diesel
  • Supply of Gasoline is the resulting amount manufactured as a result
other problems
OTHER PROBLEMS
  • 4TH Plant acquisition?
    • Production equal to F3
    • We find values: a = 48.75, b = 331.25, and c=d=337.5
    • The values for c and d are half of the original value for c we found when only 3 plants were running.
    • Allows for partial shutdown, repairs.
  • Paraffin supply:
    • a(F1) + b(F2) + c(F3) = 49(3p) + 332(5p) + 675(2p)
    • Total production of 3157 gallons of paraffin per day
selling factory 1
SELLING FACTORY #1
  • Cannot meet current daily demand for motor oil without excess production of diesel and gasoline
  • Suggest meeting demand for diesel and gasoline, and selling whatever amount of motor oil is produced with the number of barrels supplied:
    • Set up augmented matrix with value for motor oil set to variable
    • Solve for diesel and gasoline.
    • Values found: a = 364, b = 682, (variable for M = 4184)
    • These numbers of barrels will meet supply of diesel and gasoline without excess production, yet will only produce 4184 gal of Motor Oil.
  • Note that utilizing F4 would not help in the production of Motor oil without producing excess diesel and gasoline.
conclusion
CONCLUSION
  • Each plant has a unique # of barrels needed to produce current daily demand.
  • Modest changes in demand can be met with all 3 plants in operation.
  • Changes in production capability can drastically alter the company’s ability to meet demand.
  • Finding buyers for waste products (such as paraffin) may be beneficial.
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