An oil company wants to create lube oil, gasoline and diesel fuel at two refineries. There are two sources of crude oil. Consider arc 2-4. The per unit shipping cost of crude B from source 2 (node 2) to refinery 2 (node 4) is $11 and the yield is 85 percent. The following network representation depicts this problem. What is the balance of flow constraint for node 3 (Refinery 1)? A) X₁₃ + X₂₃ - .95 X₃₅ - .90 X₃₆ - .90 X₃₇ = 0 B) .80 X₁₃ + .95 X₂₃-X₃₅ -X₃₆-X₃₇ = 0 C) .80 X₁₃ + .95 X₂₃ - .90 X₃₆ - .90 X₃₇ $\ge$ 0 D) X₁₃ + X₂₃ -X₃₅ - X₃₆ - X₃₇ $\ge$ 0

Question

Quizplus · Accepted Answer

The balance of flow constraint for the Refinery 1 (node 3) should include the inflow of crude oil (XS1U1B113S1U1B0 from source 1 and XS1U2B243S1U1B0 from source 2), the outflow of lube oil (XS1F1S113S1F1S1), gasoline (XS1F2S113S1F2S1), and diesel fuel (XS1F3S113S1F3S1), and the amount of crude oil processed by Refinery 1 (XS1U1B135S1U1B0) which is indicated by its yield of 80% (0.80 XS1U1B113S1U1B0 + 0.95 XS1U1B123S1U1B0). Therefore, the balance of flow constraint for node 3 is as follows:
0.80 XS1U1B113S1U1B0 + 0.95 XS1U1B123S1U1B0 - XS1F1S113S1F1S1 - XS1F2S113S1F2S1 - XS1F3S113S1F3S1 - XS1U1B135S1U1B0 = 0. 
Options A and D are incorrect since they do not include the yield factor for crude oil processed by Refinery 1. Option C is incorrect because it includes a greater than or equal to symbol instead of an equal sign in the balance of flow constraint for node 3.

An Oil Company Wants to Create Lube Oil, Gasoline and Diesel