Assignment 1.docx - Assignment 1 Q1(a Step 1 Decision variables X1r = litres of type 1 oil in regular gasoline X2r = litres of type 2 oil in regular

# Assignment 1.docx - Assignment 1 Q1(a Step 1 Decision...

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Assignment 1 Q1: (a) Step 1. Decision variables: X 1 r = litres of type 1 oil in regular gasoline X 2 r = litres of type 2 oil in regular gasoline X 1h = litres of type 1 oil in high – octane gasoline X 2h = litres of type 2 oil in high – octane gasoline Step 2. Objective: minimize cost Step 3. Constraints: Regular gasoline is at least 40% of ingredient A High-octane gasoline is at most 50% of ingredient B Daily demand for regular gasoline ≥ 800,000 litres Daily demand for high-octane gasoline 500,000 litres Step 4. Math: Min Z = 0.1 (X 1r + X 1h ) + 0.15 (X 2r +X 2h ) S.T. 0.2 X 1r + 0.5 X 2r ≥ 0.4(X 1r + X 2r ) 0.6 X 1h + 0.3 X 2h ≤ 0.5(X 1h + X 2h ) X 1r + X 2r ≥ 800,000 X 1h + X 2h ≥ 500,000 All variables ≥ 0 To better input the data in the Excel QM, we transform the above formulas to an appropriate form: Min Z = 0.1X 1r + 0.15X 2r + 0.1X 1h + 0.15X 2h S.T. -0.2 X 1r + 0.1 X 2r ≥ 0 -0.1 X 1h + 0.2 X 2h ≥ 0 1
X 1r + X 2r ≥ 800,000 X 1h + X 2h ≥ 500,000 All variables ≥ 0 (b) From the Excel QM, we know that optimal litres of crude oil will be used to produce regular gasoline is 266,667 litres of type 1 and 533,333 litres of type 2, the optimal

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• Christopher O'Donnell

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