Recall the Bollen Oil problem from class. We took crude from one of three sources (Venezuelan Sweet, Alberta Medium, and Arabian Light). We refine this by send the crude through either a cat cracking process or through a distillation process. Our decision variables, therefore, were six: how many barrels of each of the three crude sources to send through each of the refining process (e.g. VSD = # of barrels per day to be distilled). There were only 30,000 barrels of Venezuelan Sweet available per day and only 25,000 barrels of Arabian Light Distillation could handle 40,000 barrels per day while cat cracking could handle at most 25,000 barrels per day. The products were refined from each process into gas, lube oil or bunker fuel. Each process produced this in different proportions. There was also a blending constraint for maximum sulfur content in gasoline, but we will ignore that. The costs for each type of crude and the cost to refine were different. There were minimum demands for gasoline (12,000) and lube oil (28,000). The Sensitivity output from this problem is shown below. Name VSD VSC Cell $B$3 $C$3 $D$3 $E$3 $F$3 $G$3 Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease 30000 0 5.05 1E+30 0.1 0 -0.1 5.15 0.1 1E+30 0 -0.4 4.1 0.4 1E+30 0 -0.4 4.3 0.4 1E+30 10000 0 0.1 0.4 25000 0 4.7 1E+30 0.1 ALD ALC AMD 4.5 AMC Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $H$12 gas demand 17000 0 12000 5000 1 E+30 $H$13 lube oil demand 37500 0 28000 9500 1E+30 $H$6 VS availability 30000 0.55 30000 10000 30000 $H$7 AL availability 0 0 25000 1E+30 25000 $H$9 distillation capacity 40000 4.5 40000 1E+30 10000 $H$10 cat cracking capacity 25000 4.7 25000 1E+30 13571.42857 Use this Sensitivity Analysis to answer this and the next few questions. What is the final recommended solution (i.e. how many barrels of each crude went to each refining source)? QUESTION 9 Due to maintenance, cat cracking will only be available to process 25,000 barrels per day. Does this change your solution? Explain. If it changes, provide the change in then objective functic value, if possible. QUESTION 10 Suppose the distillation could only process 35,000 barrels per day. Does the solution change? If it changes, provide the change in then objective function value, if possible. TT T Arial 3 (12pt) T QUESTION 11 Suppose that more barrels of Arabian Light were available for purchase (beyond the 25,000 already available). What is the most Bollen would be willing to pay for a barrel? Explain. TTT Arial 3 (12pt) T. QUESTION 12 Suppose the cost to send a barrel of Venezuelan Sweet through the cat cracker were to decrease by twenty cents. Would this change the solution? Explain. Arial 3 (12pt) T.EE 4 point QUESTION 13 Suppose the cost to send a barrel of Arabian Light through the cat cracker were to increase by fifty cents. Would this change the solution? Explain. Arial 3 (12pt) T-SE Recall the Bollen Oil problem from class. We took crude from one of three sources (Venezuelan Sweet, Alberta Medium, and Arabian Light). We refine this by send the crude through either a cat cracking process or through a distillation process. Our decision variables, therefore, were six: how many barrels of each of the three crude sources to send through each of the refining process (e.g. VSD = # of barrels per day to be distilled). There were only 30,000 barrels of Venezuelan Sweet available per day and only 25,000 barrels of Arabian Light Distillation could handle 40,000 barrels per day while cat cracking could handle at most 25,000 barrels per day. The products were refined from each process into gas, lube oil or bunker fuel. Each process produced this in different proportions. There was also a blending constraint for maximum sulfur content in gasoline, but we will ignore that. The costs for each type of crude and the cost to refine were different. There were minimum demands for gasoline (12,000) and lube oil (28,000). The Sensitivity output from this problem is shown below. Name VSD VSC Cell $B$3 $C$3 $D$3 $E$3 $F$3 $G$3 Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease 30000 0 5.05 1E+30 0.1 0 -0.1 5.15 0.1 1E+30 0 -0.4 4.1 0.4 1E+30 0 -0.4 4.3 0.4 1E+30 10000 0 0.1 0.4 25000 0 4.7 1E+30 0.1 ALD ALC AMD 4.5 AMC Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $H$12 gas demand 17000 0 12000 5000 1 E+30 $H$13 lube oil demand 37500 0 28000 9500 1E+30 $H$6 VS availability 30000 0.55 30000 10000 30000 $H$7 AL availability 0 0 25000 1E+30 25000 $H$9 distillation capacity 40000 4.5 40000 1E+30 10000 $H$10 cat cracking capacity 25000 4.7 25000 1E+30 13571.42857 Use this Sensitivity Analysis to answer this and the next few questions. What is the final recommended solution (i.e. how many barrels of each crude went to each refining source)? QUESTION 9 Due to maintenance, cat cracking will only be available to process 25,000 barrels per day. Does this change your solution? Explain. If it changes, provide the change in then objective functic value, if possible. QUESTION 10 Suppose the distillation could only process 35,000 barrels per day. Does the solution change? If it changes, provide the change in then objective function value, if possible. TT T Arial 3 (12pt) T QUESTION 11 Suppose that more barrels of Arabian Light were available for purchase (beyond the 25,000 already available). What is the most Bollen would be willing to pay for a barrel? Explain. TTT Arial 3 (12pt) T. QUESTION 12 Suppose the cost to send a barrel of Venezuelan Sweet through the cat cracker were to decrease by twenty cents. Would this change the solution? Explain. Arial 3 (12pt) T.EE 4 point QUESTION 13 Suppose the cost to send a barrel of Arabian Light through the cat cracker were to increase by fifty cents. Would this change the solution? Explain. Arial 3 (12pt) T-SE