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 flowchart depicts this problem. What is the balance of flow constraint for node 7 (Diesel)? A)X₃₅ + X₃₆ + X₃₇ = 75 B)X₃₇ + X₄₇ $\ge$ 75 C).90 X₃₇ + .95 X₄₇ = 75 D)X₃₇ + X₄₇ -X₃₆ - X₃₅ - X₄₅ - X₄₆ $\ge$75

Question

Quizplus · Accepted Answer

The balance of flow constraint for node 7 (Diesel) is the total amount of diesel fuel produced. Since there are two sources of crude oil, we need to consider the yield from each source. From the flowchart, we can see that diesel fuel is produced from two intermediate products, X₃₇ and X₄₇. According to the problem statement, crude B from source 2 (node 2) has a yield of 85%, so the amount of X₃₇ produced from this source would be 0.85*X₃₇. Similarly, crude A from source 1 (node 1) has a yield of 90%, so the amount of X₄₇ produced from this source would be 0.90*X₄₇. Therefore, the balance of flow constraint for node 7 can be written as: 0.85*X₃₇ + 0.90*X₄₇ = 75 Simplifying this equation, we get: 0.85 X₃₇ + 0.90 X₄₇ = 75

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