5) The ABC Oil Company produces 4 products (gasoline, heating oil, jet fuel, and

Question

5) The ABC Oil Company produces 4 products (gasoline, heating oil, jet fuel, and lubricating oil). These products are made from 4 available crude oils. There are two processing units. Unit one can process any of the 4 crude oils (1.2,3 4) unt to only processecre 4. The availability of crude oil (barrels per week) is shown below Crude barrels/wk 200,000 150,000 200,000 250,000 4 The input-output table below shows the relationship between each crude oil and its products. For example, 1 barrel of crude 1 can produce 0.5 barrel of gasoline, 3 barrel of heating oil, no lub oil, 1 barrel of jet fuel, and.1 barrel loss. Gasoline Heating Lub Oil Jet Fuel Loss 0.100.10 0.20 0.100.10 0.20 Unit 1 Oil Crude 1 0.50 Crude 2 0.40 Crude 3 0.60 Crude 4 0.50 0.30 0.20 0.20 0.10 0.20 0.20 0.10 0.0 Unit 2 Crude 4 0.40 0.10 0.30 0.10 In unit 1, the profit per barrel refined is 15 cents for crude 1, 20 cents for crude 2, 11 cents for crude 3, and 20 cents for crude 4. In unit 2, each barrel refined produces a profit of 30 cents. Marketing has indicated that weekly demands are as follows: up to 250,000 barrels of gasoline, 120,000 barrels of heating oil, 30,000 barrels of lub oil, and 100,000 barrels of jet fuel. Let X1 = amount of crude 1 processed X2 amount of crude 2 processed X3 = amount of crude 3 processed X4 = amount of crude 4 processed at unit 1 x5 = amount of crude 4 processed at unit 2 Write out the objective function and constraint set for this problem.

Explanation / Answer

objective function is to maximize profit(Z)

max Z=(15x1+20x2+11x3+20x4)+(30x5)

constraints are

x1<=200000

x2<=150000

x3<=200000

x4+x5<=250000

0.5x1+0.4x2+0.6x3+0.5x4+0.4x5<=250000

0.3x1+0.2x2+0.2x3+0.1x4+0.1x5<=120000

0.3x5<=30000

0.1x1+0.2x2+0.1x3+0.2x4+0.2x5<=120000

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